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Group whose operation is a composition of braids
In mathematics, the braid group on n strands (denoted B n {\displaystyle B_{n}} ), also known as the Artin braid group, is the group whose elements are
Braid_group
Structure of strands of flexible material
range of structures (such as a fishtail braid, a five-stranded braid, rope braid, a French braid and a waterfall braid). The structure is usually long and
Braid
Mathematical representation
In mathematics the Burau representation is a representation of the braid groups, named after and originally studied by the German mathematician Werner
Burau_representation
Three dimensional group structure
The loop braid group is a mathematical group structure that is used in some models of theoretical physics to model the exchange of particles with loop-like
Loop_braid_group
Generalized Braid group on the Sphere
spherical braid group or Hurwitz braid group is a braid group on n strands. In comparison with the usual braid group, it has an additional group relation
Spherical_braid_group
Concept in mathematics
the classifying space of the n {\displaystyle n} th braid group (see below). The n-strand braid group on a connected topological space X is B n ( X ) :=
Configuration space (mathematics)
Configuration_space_(mathematics)
Possible statistical behavior of particles in quantum statistical mechanics
theoretical physics, braid statistics is a generalization of the spin statistics of bosons and fermions based on the concept of braid group. While for fermions
Braid_statistics
In mathematics, a double affine braid group is a group containing the braid group of an affine Weyl group. Their group rings have quotients called double
Double_affine_braid_group
Family of infinite discrete groups
mathematical area of group theory, Artin groups, also known as Artin–Tits groups or generalized braid groups, are a family of infinite discrete groups defined by
Artin–Tits_group
Group of symmetries of an n-dimensional hypercube
(finite) symmetric group is the braid group on n strands. Not all Artin–Tits groups have a natural representation in terms of geometric braids. However, the
Hyperoctahedral_group
Orientation-preserving mapping class group of the torus
center; equivalently, to the group of inner automorphisms of B3. The braid group B3 in turn is isomorphic to the knot group of the trefoil knot. The quotients
Modular_group
In mathematics, an affine braid group is a braid group associated to an affine Coxeter system. Their group rings have quotients called affine Hecke algebras
Affine_braid_group
American mathematician
she published "On Braid Groups", which introduced a way to relate the mapping class group of a surface to the mapping class group of a punctured version
Joan_Birman
American emo band
Braid is an American emo band from Champaign, Illinois, formed in 1993. Following several early line-up changes, the band eventually settled on Bob Nanna
Braid_(band)
Branch of mathematics that studies the properties of groups
term group-based cryptography refers mostly to cryptographic protocols that use infinite non-abelian groups such as a braid group. List of group theory
Group_theory
Concept in mathematics
class group of surfaces are related to various other groups, in particular braid groups and outer automorphism groups. The mapping class group appeared
Mapping class group of a surface
Mapping_class_group_of_a_surface
Mathematical group
A generalized braid group is said to be of spherical type if the associated Coxeter group is finite. If B is a generalized braid group of spherical type
Parabolic subgroup of a reflection group
Parabolic_subgroup_of_a_reflection_group
Application of group theory to cryptography
mostly to cryptographic protocols that use infinite non-abelian groups such as a braid group. Shpilrain–Zapata public-key protocols Magyarik–Wagner public
Group-based_cryptography
Hairstyle formed by interlacing three or more Strands
Braids (also referred to as plaits) are a hairstyle formed by interlacing three or more strands of hair. Braiding has been used to style and ornament
Braid_(hairstyle)
Object in category theory
identities defined below. The term braided references the fact that the braid group plays an important role in the theory of braided monoidal categories. Partly
Braided_monoidal_category
In the mathematical area of braid theory, the Dehornoy order is a left-invariant total order on the braid group, found by Patrick Dehornoy. Dehornoy's
Dehornoy_order
Quantum consistency equation
Yang–Baxter equation also shows up when discussing knot theory and the braid groups where R {\displaystyle R} corresponds to swapping two strands. Since
Yang–Baxter_equation
Mathematical invariant of a knot or link
is the trace closure of a braid, say with n strands. Now define a representation ρ {\displaystyle \rho } of the braid group on n strands, Bn, into the
Jones_polynomial
Mathematical monograph on braid groups
Braids, Links, and Mapping Class Groups is a mathematical monograph on braid groups and their applications in low-dimensional topology. It was written
Braids, Links, and Mapping Class Groups
Braids,_Links,_and_Mapping_Class_Groups
Number line and triangular tiling's symmetry mathematical structure
third relation are sometimes called the braid relations.) When n = 2 {\displaystyle n=2} , the affine symmetric group S ~ 2 {\displaystyle {\widetilde {S}}_{2}}
Affine_symmetric_group
Topics referred to by the same term
Braid Hills Braid Burn Braid theory, an abstract geometric theory in the field of topology Braid group, a type of object in braid theory Braid (band), an
Braid_(disambiguation)
Type of two-dimensional quasiparticle
dimensions the group of permutations of two particles is no longer the symmetric group S2 (with two elements) but rather the braid group B2 (with an infinite
Anyon
British-Israeli mathematician
introduced, among other things, certain novel linear representations of the braid group – known as Lawrence–Krammer representations. In papers published in 2000
Ruth_Lawrence
use of braid groups to develop cryptographic protocols. Later several other non-commutative structures like Thompson groups, polycyclic groups, Grigorchuk
Non-commutative_cryptography
Particle
depth of the resulting compiled braids. Algorithm of is informed by number-theoretical properties of the anyonic braid group representations that are specific
Fibonacci_anyons
Type of mathematical group
set of generators for a given arithmetic group. Braid groups (which are defined as a finitely presented group) have faithful linear representation on a
Linear_group
Topics referred to by the same term
A braid algebra can be: A Gerstenhaber algebra (also called an antibracket algebra). An algebra related to the braid group. This disambiguation page lists
Braid_algebra
Ankeny–Artin–Chowla congruence Artin algebra Artin billiards Artin braid group Artin character Artin conductor Artin's conjecture for conjectures by
List of things named after Emil Artin
List_of_things_named_after_Emil_Artin
introduced, among other things, certain novel linear representations of the braid group — known as Lawrence–Krammer representation. In papers published in 2000
List of inventions and discoveries by women
List_of_inventions_and_discoveries_by_women
Type of quantum computer
world lines intertwine to form braids in a three-dimensional spacetime (one temporal and two spatial dimensions). The braids act as the logic gates of the
Topological_quantum_computer
Simplest non-trivial closed knot with three crossings
{\displaystyle \langle x,y\mid xyx=yxy\rangle .} This group is isomorphic to the braid group with three strands. As the simplest nontrivial knot, the
Trefoil_knot
Type of group in abstract algebra
symmetric group over an arbitrary field is widely regarded as one of the most important open problems in representation theory. Braid group History of group theory
Symmetric_group
Gives necessary and sufficient conditions for two braids to have equivalent closures
for two braids to have closures that are equivalent knots or links. The conditions are stated in terms of the group structures on braids. Braids are algebraic
Markov_theorem
Algebra term in mathematics
the Hecke algebra of an affine Weyl group, given as the quotient of the group ring of a double affine braid group. They were introduced by Cherednik,
Double_affine_Hecke_algebra
Type of group used in topology and geometric group theory
The braid groups B n {\displaystyle B_{n}} , for n ≤ 6 {\displaystyle n\leq 6} , are known to be CAT(0). It is conjectured that all braid groups are CAT(0)
CAT(0)_group
Scottish judge
Peter Braid, Lord Braid is a Scottish judge who has been a Senator of the College of Justice since 23 June 2020. Braid graduated from the University of
Peter_Braid,_Lord_Braid
Quotient of a weakly contractible space by a free action
{UConf} _{n}(\mathbb {R} ^{2})} is the classifying space of the Artin braid group B n {\displaystyle B_{n}} , and the ordered configuration space Conf
Classifying_space
American mathematician
group of surfaces, including braid groups, and their relationship to automorphism groups of free groups and arithmetic groups. She is a professor of mathematics
Tara_E._Brendle
Algebraic construct of interest in theoretical physics
the braid group, and to define quasi-invariants for knots, links and braids. Masaki Kashiwara has researched the limiting behaviour of quantum groups as
Quantum_group
Mathematical group of the homotopy classes of loops in a topological space
group of the trefoil knot is known to be the braid group B 3 {\displaystyle B_{3}} , which gives another example of a non-abelian fundamental group.
Fundamental_group
French mathematician (b. 1977)
open questions about symplectic 4-manifolds, singular plane curves, and braid group factorizations". arXiv:math/0410119. (published in 2005 in Proceedings
Denis_Auroux
African hairstyle originating from the Fulani ethnic group
Fulani braids (also known as Fulani style, Fulani hairstyle) are a hair-braiding style originating from the Fulani people, a nomadic ethnic group who inhabit
Fulani_braids
present a representation of the braid group. As first example, every vector space is braided via the trivial braiding (simply flipping)[clarification
Braided_vector_space
Fundamental group of a knot complement
algorithm. The unknot has knot group isomorphic to Z. The trefoil knot has knot group isomorphic to the braid group B3. This group has the presentation ⟨ x
Knot_group
Generalization of associativity properties
by the Artin braid group B n {\displaystyle B_{n}} . Moreover, this non- Σ {\displaystyle \Sigma } operad has the structure of a braided operad, which
Operad
Type of mathematical theorem
infinite symmetric group". Ann. Math. 2. 73: 229–257. doi:10.2307/1970333. Arnol’d, V.I. (1969). "The cohomology ring of the colored braid group". Mathematical
Homological_stability
Branch of topology
topics are the theory of 3-manifolds and 4-manifolds, knot theory, and braid groups. This can be regarded as a part of geometric topology. It may also be
Low-dimensional_topology
Partial differential equations of correlation functions
algebra agrees with the linear representation of braid group given by R-matrix of the corresponding quantum group. In the case when the underlying Lie algebra
Knizhnik–Zamolodchikov equations
Knizhnik–Zamolodchikov_equations
Every knot or link can be represented as a closed braid
states that every knot or link can be represented as a closed braid; that is, a braid in which the corresponding ends of the strings are connected in
Alexander's_theorem
Element of algebraic structure
problem and conjugacy problem. Examples of such groups include braid groups and, more generally, Artin groups of finite Coxeter type. The name was coined
Garside_element
Braid group representation
mathematics the Lawrence–Krammer representation is a representation of the braid groups. It fits into a family of representations called the Lawrence representations
Lawrence–Krammer representation
Lawrence–Krammer_representation
Deformation of the group algebra of a Coxeter group
algebra of a Coxeter group. Hecke algebras are quotients of the group rings of Artin braid groups. This connection found a spectacular application in Vaughan
Iwahori–Hecke_algebra
relations. For example, a free group is a group on a set of generators with no relations, whereas a braid group is a group on generators g i {\displaystyle
Infinite_group
group homomorphism) from a Coxeter group to the corresponding braid group, taking any element of the Coxeter group represented by some reduced word in
Matsumoto's theorem (group theory)
Matsumoto's_theorem_(group_theory)
Interlinked multi-loop construction where cutting one loop frees all the others
Brunnian braid is a braid that becomes trivial upon removal of any one of its strings. Brunnian braids form a subgroup of the braid group. Brunnian braids over
Brunnian_link
Concept in topological group theory
isomorphic to the braid group on three strands. The above definitions and constructions all apply to the special case of Lie groups. In particular, every
Covering_group
Mathematical behavior near singularities
leading to the Riemann existence theorem. Braid group Monodromy matrix Monodromy theorem Mapping class group (of a punctured disk) König, Wolfgang; Sprekels
Monodromy
Algebra in statistical mechanics
It is also related to integrable models, knot theory and the braid groups, quantum groups and subfactors of von Neumann algebras. Let R {\displaystyle
Temperley–Lieb_algebra
Topological space with only one nontrivial homotopy group
{\displaystyle K(P_{n},1)} , where P n {\displaystyle P_{n}} is the pure braid group on n {\displaystyle n} strands. Correspondingly, the nth unordered configuration
Eilenberg–MacLane_space
British mathematician
K3 fibrations'. Motivated by homological mirror symmetry, he produced braid group actions on derived categories of coherent sheaves in joint work with
Richard Thomas (mathematician)
Richard_Thomas_(mathematician)
Concept in mathematics
Reflection Groups, pp.91-93 Broué, Michel; Malle, Gunter; Rouquier, Raphaël (1995), "On complex reflection groups and their associated braid groups" (PDF)
Complex_reflection_group
algebra, the Nichols algebra of a braided vector space (with the braiding often induced by a finite group) is a braided Hopf algebra which is denoted by
Nichols_algebra
Australian mathematician
University of California, Santa Barbara. He is known for his proof that braid groups are linear, concurrently with and independently of another proof by Daan
Stephen_Bigelow
American mathematician
representation theory of braid groups. In 2013 he became a fellow of the American Mathematical Society, for "contributions to group theory, number theory
Michael_J._Larsen
2004 live album by David Braid
David Braid Sextet Live is the second album by Canadian jazz pianist and composer, David Braid, as well as the second album to feature the group the David
Vivid: The David Braid Sextet Live
Vivid:_The_David_Braid_Sextet_Live
Style of hair braiding
called canerows in the Caribbean) are a style of three-strand braids in which the hair is braided very close to the scalp, using an underhand, upward motion
Cornrows
Group of real 2×2 matrices with unit determinant
of the modular group PSL(2, Z) is the braid group on 3 generators, B3, which is the universal central extension of the modular group. These are lattices
SL2(R)
Canadian musical group
Braided is a musical group consisting of Casey LeBlanc, Ashley Leitão, and Amber Fleury, who all competed on the third season of Canadian Idol in 2005
Braided
Canadian composer and jazz pianist
David Braid (born 25 March 1975 in Hamilton, Ontario) is a Canadian composer and pianist. Canadian composer and jazz pianist, David Braid, is "considered
David_Braid
Russian mathematician (born 1954)
"Review of 2 books: Braid groups by Christian Kassel and Vladimir Turaev (with the graphical assistance of Olivier Douane); Ordering braids by Patrick Dehornoy"
Vladimir_Turaev
The Hermitage of Braid is an area between the Braid Hills and Blackford Hill in Edinburgh, Scotland. The Braid Burn runs through it and it has large sections
Hermitage_of_Braid
Knitting style
increases, the number of crossing patterns increases, as described by the braid group. Various visual effects are also possible by shifting the center lines
Cable_knitting
Periodic solution to the n-body problem
that this topology is linked to certain cosets of the pure braid group in the full braid group, as well as the centralizers of elements within the corresponding
N-body_choreography
quotient of the group algebra of the braid group, so representations of the Temperley–Lieb algebra give representations of the braid group, which in turn
Subfactor
Cryptographic protocol
\beta } in the braid group, and T-values, one applies E-multiplication by converting the generator to a colored Burau matrix and braid permutation, (
Algebraic_Eraser
American mathematician
S2CID 119485709. R. Laver (1996). "Braid group actions on left distributive structures, and well orderings in the braid groups". Journal of Pure and Applied
Richard_Laver
Area in mathematics devoted to the study of finitely generated groups
Free-by-cyclic groups One-relator groups Hyperbolic groups Mapping class groups (automorphisms of surfaces) Symmetric groups Braid groups Coxeter groups General
Geometric_group_theory
American mathematician (born 1947)
Michael Anshel, both mathematicians, Dorian Goldfeld founded the field of braid group cryptography. In 1987 he received the Frank Nelson Cole Prize in Number
Dorian_M._Goldfeld
Theory in number theory
geometry is in some of such combinatorial ideas of the arithmetic of braid groups and their Lie algebras of Makoto Matsumoto et al., then later in Mochizuki's
Anabelian_geometry
Moduli spaces of ramified covers
The fundamental group of the (topological) configuration space Conf n {\displaystyle \operatorname {Conf} _{n}} is the Artin braid group B n {\displaystyle
Hurwitz_space
Project by NIST to standardize post-quantum cryptography
considered whilst standardizing. On July 5, 2022, NIST announced the first group of winners from its six-year competition. On July 5, 2022, NIST announced
NIST Post-Quantum Cryptography Standardization
NIST_Post-Quantum_Cryptography_Standardization
group of a braid group (or any subgroup of a braid group) is trivial. This was proved by F. Thomas Farrell and Sayed K. Roushon. The Whitehead group of
Whitehead_torsion
Unique knot with a crossing number of four
closed braid (namely, the closure of the 3-string braid σ1σ2−1σ1σ2−1), and a theorem of John Stallings shows that any closed homogeneous braid is fibered
Figure-eight knot (mathematics)
Figure-eight_knot_(mathematics)
Study of mathematical knots
methods from knot theory have been applied to quantum computing, where braid group representations serve as a model for topological qubits, and to materials
Knot_theory
German physicist
spaces also led to an understanding of the occurrence of braid group statistics and quantum groups. In quantum statistical mechanics, Haag, together with
Rudolf_Haag
1998 studio album by Braid
Frame & Canvas is the third studio album by American rock band Braid. It was released on April 7, 1998, through Polyvinyl Record Co. After the release
Frame_&_Canvas
Device that interlaces strands of yarn or wire
A braiding machine is a device that interlaces three or more strands of yarn or wire to create a variety of materials, including rope, reinforced hose
Braiding_machine
Theory of the strong nuclear interactions
flux-line lattices are described by Emil Artin's braid group, which is nonabelian, since one braid can wind around another one. Campbell, John; Huston
Quantum_chromodynamics
from the original on 2021-04-06. Retrieved 2023-10-31. Her blond hair was braided and piled atop her head in the German style called Gretchen frisur. Loussouarn
List_of_hairstyles
stratified spaces has uses everywhere from pure mathematics topics such as braid groups and representations to robot motion planning and potential theory. A
Stratified_Morse_theory
Thompson group (finite) Tits group Weyl group Arithmetic group Braid group Burnside's lemma Cayley's theorem Coxeter group Crystallographic group Crystallographic
List_of_group_theory_topics
|w'|_{X}^{2}\}\right)} . The Garside algorithm for solving the conjugacy problem in braid groups has a similar general structure to Whitehead's algorithm, with "cycling
Whitehead's_algorithm
denominator closure Tangle numerator closure Reciprocal tangle Braid theory Braid group Band sum Flype Fox n-coloring Tricolorability Knot sum Reidemeister
List_of_knot_theory_topics
French mathematician (1952–2019)
braid group. In his later career, he was a major contributor to the theory of braid groups, including creating a fast algorithm for comparing braids,
Patrick_Dehornoy
Problem on words in group theory
one-relator groups with torsion braid groups knot groups finitely presented conjugacy separable groups finitely generated abelian groups (relators include all commutators)
Conjugacy_problem
BRAID GROUP
BRAID GROUP
Boy/Male
American, Australian, British, English
Broad
Boy/Male
English
Broad; wide.
Female
English
Variant spelling of English unisex Brady, BRAIDY means "broad-chested."Â
Boy/Male
Arabic, Muslim
Another Name for God; Away; Distant
Boy/Male
Norse English German
Firebrand.
Boy/Male
English American Welsh
Broad clearing in the wood. From a surname and place name based on the Old English words for...
Boy/Male
Muslim
Leader
Girl/Female
Danish, Hindu, Indian, Marathi, Sanskrit, Tamil
Braid
Male
English
Variant spelling of English unisex Brady, possibly BRAIDY means "large-chested."Â
Boy/Male
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Parsi, Telugu
Cloud
Boy/Male
Hindu
Messenger, Partner, Cloud
Girl/Female
Celtic, French, German, Irish
Strong; Protective
Male
Portuguese
Galician-Portuguese form of Latin Blasius, BRAIS means "talks with a lisp."Â
Girl/Female
Indian, Sanskrit
Braid of Flowers
Girl/Female
Celtic Irish
Strong.
Surname or Lastname
English, Scottish, Scandinavian, North German, and Dutch
English, Scottish, Scandinavian, North German, and Dutch : from the Germanic personal name Brando, a short form of various compound personal names containing the element brand ‘sword’ (a derivative of brinnan ‘to flash’), of which the best known is Hildebrand. There is place name evidence for Brant(a) as an Old English personal name; however, the Middle English personal name Brand was probably introduced to England from Old Norse; Brandr is a common Old Norse personal name.English : topographic name for someone who lived by a place where burning had occurred, from Old English brand, or a habitational name from a minor place named with this word, as for example The Brand in Northamptonshire and Nottinghamshire.German : variant of Brandt 1.Scandinavian : from the personal name Brand, Brant, from Old Norse Brandr (see 1).Swedish : ornamental name from brand ‘fire’.Jewish (Ashkenazic) : ornamental name or nickname from German Brant ‘fire’, ‘conflagration’.
Boy/Male
American, Australian, German, Irish
High; Noble
Boy/Male
American, Anglo, Australian, British, English, German, Norse, Norwegian, Scandinavian, Swedish
Proud; Firebrand; Sword Blade; Sword; Fiery Torch; Beacon
Surname or Lastname
English
English : unexplained.Variant of Dutch Bradt.Romanian : unexplained.
Male
English
Short form of English names beginning with Brad-, from Old English brád, BRAD means "broad."
BRAID GROUP
BRAID GROUP
Boy/Male
Indian, Punjabi, Sikh
Victory of God
Female
English
English name derived from the vocabulary word fancy, which is a contracted form of fantasy, FANCY means "desire, inclination, whim."
Boy/Male
Indian, Sanskrit
Follower of the Scriptures
Boy/Male
Indian
Terrible.
Girl/Female
Dutch, German, Latin, Swedish
Worthy of Respect; Great; Magnificent; Venerable; Female Version of Gustaaf
Girl/Female
Irish American
Dark. Feminine of Ciaran. Name of a saint.
Boy/Male
Tamil
A king, Little Moon
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Lord Krishna
Girl/Female
Greek
Flower.
Boy/Male
Hindu
Moon glow, Moonlight
BRAID GROUP
BRAID GROUP
BRAID GROUP
BRAID GROUP
BRAID GROUP
v. t.
To weave, interlace, or entwine together, as three or more strands or threads; to form into a braid; to plait.
v. t.
A mark made by burning with a hot iron, as upon a cask, to designate the quality, manufacturer, etc., of the contents, or upon an animal, to designate ownership; -- also, a mark for a similar purpose made in any other way, as with a stencil. Hence, figurately: Quality; kind; grade; as, a good brand of flour.
v. t.
To braid.
n.
A quick motion; a start.
v. t.
To reproach. [Obs.] See Upbraid.
v. t.
An instrument to brand with; a branding iron.
n.
A fancy; freak; caprice.
v. t.
Deceitful.
v. t.
To mingle, or to bring to a uniformly soft consistence, by beating, rubbing, or straining, as in some culinary operations.
n.
A narrow fabric, as of wool, silk, or linen, used for binding, trimming, or ornamenting dresses, etc.
imp. &. p. p.
of Braid
n.
A plait, band, or narrow fabric formed by intertwining or weaving together different strands.
v. t.
To make a raid upon or into; as, two regiments raided the border counties.
v. i.
To start; to awake.
p. pr. & vb. n.
of Braid
n.
An attack or invasion for the purpose of making arrests, seizing property, or plundering; as, a raid of the police upon a gambling house; a raid of contractors on the public treasury.
v. t.
To haul up by the brails; -- used with up; as, to brail up a sail.
n.
A braid.
v. t.
To braid.