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Group of matrices with determinant 1
In mathematics, the special linear group SL ( n , R ) {\displaystyle \operatorname {SL} (n,R)} of degree n {\displaystyle n} over a commutative ring
Special_linear_group
Construction in group theory
the general linear group. The projective special linear group, PSL, is defined analogously, as the induced action of the special linear group on the associated
Projective_linear_group
Group of 𝑛 × 𝑛 invertible matrices
In mathematics, the general linear group of degree n {\displaystyle n} is the set of n × n {\displaystyle n\times n} invertible matrices, together with
General_linear_group
Type of mathematical group
instances are groups which are defined as subgroups of a linear group, for example: The group GLn(K) itself; The special linear group SLn(K) (the subgroup
Linear_group
Group of all affine transformations of an affine space
translations, and the affine group of A can be described concretely as the semidirect product of V by GL(V), the general linear group of V: Aff ( V ) = V ⋊
Affine_group
Concept in mathematics
model for the study of other Lie algebras. The Lie group that it generates is the special linear group. The Lie algebra s l 2 C {\displaystyle {\mathfrak
Special_linear_Lie_algebra
Subgroup of the group of invertible n×n matrices
In mathematics, a linear algebraic group is a subgroup of the group of invertible n × n {\displaystyle n\times n} matrices (under matrix multiplication)
Linear_algebraic_group
Mathematical group
the orders of such groups, with a view to classifying cases of coincidence. A classical group is, roughly speaking, a special linear, orthogonal, symplectic
Group_of_Lie_type
Five sporadic simple groups
sporadic simple group, being isomorphic to the projective special linear group PSL(3,4). Mathieu (1861, p.271) introduced the group M12 as part of an
Mathieu_group
Mathematical group
In mathematics, the symplectic group is the group of linear transformations that preserve the geometric structure of phase space, the space of position
Symplectic_group
Connected non-abelian Lie group lacking nontrivial connected normal subgroups
when it is isomorphic to the projective special linear group. The first classification of simple Lie groups was by Wilhelm Killing, and this work was
Simple_Lie_group
Mathematical group with trivial abelianization
perfect group need not be simple; for example, the special linear group over the field with 5 elements, SL(2,5) (or the binary icosahedral group, which
Perfect_group
Topics referred to by the same term
of matrices with determinant 1: Special linear group Special orthogonal group Special unitary group Special affine group This disambiguation page lists
Special_group
Mathematical finite graph-associated function
1960s in the context of discrete subgroups of the two-by-two p-adic special linear group. Jean-Pierre Serre suggested in his book Trees that Ihara's original
Ihara_zeta_function
Type of group in mathematics
setting of Lie groups, this includes the real, complex, and quaternionic general linear, special linear, orthogonal, unitary, and symplectic groups, together
Classical_group
Transformations induced by a mathematical group
or group, or ring ...). The general linear group GL(n, K) and its subgroups, particularly its Lie subgroups (including the special linear group SL(n
Group_action
Sum of elements on the main diagonal
special linear group of matrices with determinant 1. The special linear group consists of the matrices which do not change volume, while the special linear
Trace_(linear_algebra)
Group of unitary complex matrices with determinant of 1
the group that preserves the standard inner product on C n {\displaystyle \mathbb {C} ^{n}} . It is itself a subgroup of the general linear group, SU
Special_unitary_group
special linear group SL(n,C), the compact real form is the special unitary group SU(n) and the split real form is the real special linear group SL(n,R)
Real_form_(Lie_theory)
Group of real 2×2 matrices with unit determinant
In mathematics, the special linear group SL(2, R) or SL2(R) is the group of 2 × 2 real matrices with determinant one: SL ( 2 , R ) = { ( a b c d ) : a
SL2(R)
Algebraic variety with a group structure
orthogonal groups, general linear groups, projective groups, Euclidean groups, etc. Many matrix groups are also algebraic. Other algebraic groups occur naturally
Algebraic_group
Orientation-preserving mapping class group of the torus
In mathematics, the modular group is the projective special linear group PSL ( 2 , Z ) {\displaystyle \operatorname {PSL} (2,\mathbb {Z} )} of 2 × 2
Modular_group
Zariski topology. Special groups include the general linear group, the special linear group, and the symplectic group. Special groups are necessarily connected
Special group (algebraic group theory)
Special_group_(algebraic_group_theory)
Nonabelian group in algebraic group theory
One can show that the binary tetrahedral group is isomorphic to the special linear group SL(2,3) – the group of all 2 × 2 matrices over the finite field
Binary_tetrahedral_group
Type of mathematical space
for the special linear group over F. Other flag varieties arise by considering partial flags, or by restriction from the special linear group to subgroups
Generalized_flag_variety
Mathematical study of invariants under symmetries
under the transformations from a given linear group. For example, if we consider the action of the special linear group SLn on the space of n by n matrices
Invariant_theory
Integral transform
3-dimensional family, and can be visualized as the action of the special linear group SL2(C) on the time–frequency plane (domain). As this defines the
Linear canonical transformation
Linear_canonical_transformation
Sporadic simple group
projective special linear group of 3-dimensional space over the finite field with 4 elements (Dixon & Mortimer 1996, pp. 192–205). This group, sometimes
Mathieu_group_M24
Modular function in mathematics
j-invariant or j function is a modular function of weight zero for the special linear group SL ( 2 , Z ) {\displaystyle \operatorname {SL} (2,\mathbb {Z} )}
J-invariant
Undeciphered writing system of ancient Crete
were four major branches of this group: Linear A, Linear B, Cypro-Minoan, and Cretan hieroglyphic. In the 1950s, Linear B was deciphered and its underlying
Linear_A
Concept in topological group theory
of SO(n). For n ≥ 2, the universal cover of the special linear group SL(n, R) is not a matrix group (i.e. it has no faithful finite-dimensional representations)
Covering_group
Mathematical group based upon a finite number of elements
systematic exploration of finite groups of Lie type started with Camille Jordan's theorem that the projective special linear group PSL(2, q) is simple for q
Finite_group
Topics referred to by the same term
(elliptic function), sine lemniscate function Special linear group in mathematics, denoted SLn or SL(n) Special linear Lie algebra, denoted s l n ( F ) {\displaystyle
SL
Group that is also a differentiable manifold with group operations that are smooth
exponential map. The following are standard examples of matrix Lie groups. The special linear groups over R {\displaystyle \mathbb {R} } and C {\displaystyle
Lie_group
Group without normal subgroups other than the trivial group and itself
second smallest nonabelian simple group is the projective special linear group PSL(2,7) of order 168, and every simple group of order 168 is isomorphic to
Simple_group
{\displaystyle GL(n,\mathbb {C} )} are equivalent as representations of the special linear group S L ( n , C ) {\displaystyle SL(n,\mathbb {C} )} if and only if there
Representations of classical Lie groups
Representations_of_classical_Lie_groups
Type of group in abstract algebra
theory of Coxeter groups, the symmetric group is the Coxeter group of type An and occurs as the Weyl group of the general linear group. In combinatorics
Symmetric_group
Relativistic wave equation describing massless fermions
transform by means of the double covering of the Lorentz group by the special linear group S L ( 2 , C ) {\displaystyle \mathrm {SL} (2,\mathbb {C} )}
Weyl_equation
Structure group sub-bundle on a tangent frame bundle
orthogonal group, an O ( n ) {\displaystyle \operatorname {O} (n)} -structure defines a Riemannian metric, and for the special linear group an SL (
G-structure_on_a_manifold
complex special linear group is a subgroup of the general linear group with the same nilpotent orbits. However, if we replace the complex special linear group
Nilpotent_orbit
PSL2(q) The projective special linear groups PSL3(p) for p = 1 + 2a or p = 1 + 2a3, and PSL3(4) The projective special unitary groups PSU3(p) for p = 1 - 2a
Thin group (finite group theory)
Thin_group_(finite_group_theory)
with the map from a special linear group over a finite field to the projective special linear group. For n = 3, the symmetric group is SL(2, 2) ≅ PSL(2
Covering groups of the alternating and symmetric groups
Covering_groups_of_the_alternating_and_symmetric_groups
Upper-half plane model of hyperbolic non-Euclidean geometry
a linear fractional transformation of complex numbers, and the hyperbolic motions are represented by elements of the projective special linear group
Poincaré_half-plane_model
Automorphism group of the Klein quartic
In mathematics, the projective special linear group PSL(2, 7), isomorphic to GL(3, 2), is a finite simple group that has important applications in algebra
PSL(2,7)
Block design in combinatorial mathematics
form a group under composition which is the projective special linear group PSL(2,11) of order 660. There are exactly five elements of this group that leave
Steiner_system
Smallest normal subgroup by which the quotient is commutative
G^{(1)}=G} , it is called a perfect group. This includes non-abelian simple groups and the special linear groups SL n ( k ) {\displaystyle \operatorname
Commutator_subgroup
Lie groups and their associated Lie algebras
table of some common Lie groups and their associated Lie algebras. The following are noted: the topological properties of the group (dimension; connectedness;
Table_of_Lie_groups
Class of mathematical groups
the projective special linear groups PSL2(9) the projective special linear groups PSL2(2n) for n≥2 the projective special linear groups PSL3(2n) for n≥1
C-group
Natural number
algebra A 6 {\displaystyle A_{6}} through the special linear group and its corresponding special linear Lie algebra. In the third dimension, there are
63_(number)
{\displaystyle S_{4}} is an example of a monomial group that is neither supersolvable nor an A-group. The special linear group SL 2 ( F 3 ) {\displaystyle \operatorname
Monomial_group
Concept in mathematical group theory
the binary icosahedral group (which is in fact its UCE) is superperfect. More generally, the projective special linear groups PSL(n, q) are simple (hence
Superperfect_group
Topics referred to by the same term
attractiveness scale associated with looksmaxxing PSLn, the projective special linear group Psi (disambiguation) All pages with titles beginning with PSL All
PSL
Type of group in mathematics
orthogonal group of the form is the group of invertible linear maps that preserve the form. The preceding orthogonal groups are the special case where
Orthogonal_group
Lie group of Lorentz transformations
fundamental group has order 2, and its universal cover, the indefinite spin group Spin(1, 3), is isomorphic to both the special linear group SL(2, C) and
Lorentz_group
Natural number
in mathematics ranging from the fact that the abelianization of special linear group SL ( 2 , Z ) {\displaystyle \operatorname {SL} (2,\mathrm {Z} )}
12_(number)
binary form in two variables x and y that remains invariant under the special linear group acting on the variables x and y. A binary form (of degree n) is a
Invariant_of_a_binary_form
Group homomorphism into the general linear group over a vector space
mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to
Group_representation
German mathematician (1882–1935)
method worked, not only for the special linear group, but also for some of its subgroups such as the special orthogonal group. Noether followed Gordan's lead
Emmy_Noether
Mathematical function that preserves angles
transformation of the upper half-plane onto the interior of a simple polygon Special linear group – transformations that preserve volume (as opposed to angles) and
Conformal_map
Sum of inverse squares of natural numbers
group SL2(R) that the Tamagawa number of the group is one. That is, the quotient of the special linear group over the rational adeles by the special linear
Basel_problem
Syllabic script used for writing Mycenaean Greek
contains Linear B Unicode characters. Without proper rendering support, you may see question marks, boxes, or other symbols instead of Linear B. Linear B is
Linear_B
Abstract regular 4-polytope
each edge. Its automorphism group has 660 elements. The automorphism group is isomorphic to the projective special linear group of the 2-dimensional vector
11-cell
Linear representation in mathematics
special representations) for algebraic groups over local fields. For the general linear group GL(2), the dimension of the Jacquet module of a special
Steinberg_representation
Group that is a topological space with continuous group operations
representations) for the semisimple Lie groups. The unitary dual is known in many cases, such as for the special linear group of degree 2 over the real numbers
Topological_group
projective special linear group. PNT – prime number theorem. PRP – probable prime. PSO – projective orthogonal group. PSU – projective special unitary group. PU
List of mathematical abbreviations
List_of_mathematical_abbreviations
Group obtained by aggregating similar elements of a larger group
isomorphic to the multiplicative group of non-zero real numbers. The group N {\displaystyle N} is known as the special linear group S L ( 3 ) {\displaystyle
Quotient_group
Group of even permutations of a finite set
alternating groups and small groups of Lie type, particularly projective special linear groups. These are: A4 is isomorphic to PSL2(3) and the symmetry group of
Alternating_group
Mathematical concept
product of the special linear group SL(n, R) and the subgroup consisting of all scalar matrices. Similarly, when n is odd the orthogonal group O(n, R) is
Direct_product_of_groups
Mathematical group
a positive square-free integer. Here, PSL denotes the projective special linear group and O d {\displaystyle {\mathcal {O}}_{d}} is the ring of integers
Bianchi_group
each cell (60). The symmetry abstract structure is the projective special linear group of the 2-dimensional vector space over the finite field of 19 elements
57-cell
Subgroup invariant under conjugation
all n × n {\displaystyle n\times n} matrices of determinant 1 (the special linear group). To see why the subgroup S L n ( R ) {\displaystyle \mathrm {SL}
Normal_subgroup
Mathematical formula for the number of Young tableaux
{\displaystyle \lambda } corresponds to an irreducible representation of the special linear group S L k ( C ) {\displaystyle \mathrm {SL} _{k}(\mathbb {C} )} , and
Hook_length_formula
Concept in mathematics
Reductive groups include some of the most important groups in mathematics, such as the general linear group GL(n) of invertible matrices, the special orthogonal
Reductive_group
Development of linear transformations forming the Lorentz group
group of motions in hyperbolic space, the Möbius group or projective special linear group, and the Laguerre group are isomorphic to the Lorentz group
History of Lorentz transformations
History_of_Lorentz_transformations
T^{*}S^{3}\rightarrow \operatorname {SL} _{2}(\mathbb {C} )} to the special linear group and through composition with the zero section 0 : S 3 → T ∗ S 3 {\displaystyle
Gopakumar–Vafa_duality
Elements taken to zero by a homomorphism
non-zero real numbers), and the kernel of the determinant is called the special linear group S L ( n , R ) {\displaystyle SL(n,\mathbb {R} )} of n × n {\displaystyle
Kernel_(algebra)
Non-abelian group of order eight
matrices have unit determinant, this is a representation of Q8 in the special linear group SL ( 2 , C ) {\displaystyle \operatorname {SL} (2,\mathbb {C} )}
Quaternion_group
Nonabelian group of order 120
One can show that the binary icosahedral group is isomorphic to the special linear group SL(2,5) — the group of all 2×2 matrices over the finite field
Binary_icosahedral_group
Hyperbolic 3-manifold proposed as a model for the shape of the universe
the upper half-plane model of hyperbolic 3-space by the projective special linear group, PSL 2 ( Z [ i ] ) {\displaystyle \operatorname {PSL} _{2}(\mathbf
Picard_horn
Universal construction of a complex Lie group from a real Lie group
original group. They are isomorphic if the original group has a quotient by a discrete normal subgroup which is linear. For compact Lie groups, the complexification
Complexification_(Lie_group)
Discrete subgroup of the real projective special linear group of dimension 2
{\displaystyle ds={\frac {1}{y}}{\sqrt {dx^{2}+dy^{2}}}.} The group PSL(2,R) acts on H {\displaystyle H} by linear fractional transformations (also known as Möbius
Fuchsian_group
group Monster group Baby Monster group Bimonster Projective group Reductive group Simple group Quasisimple group Special linear group Symmetric group
List_of_group_theory_topics
Device in the representation theory of Lie groups
theory of Lie groups, introduced by Adolf Hurwitz (1897) for the special linear group and by Hermann Weyl for general semisimple groups. It applies to
Unitarian_trick
Branch of mathematics that studies abstract algebraic structures
studies abstract algebraic structures by representing their elements as linear transformations of vector spaces. In essence, a representation makes an
Representation_theory
Mathematics term
finite groups have property (T). Simple real Lie groups of real rank at least two have property (T). This family of groups includes the special linear groups
Kazhdan's_property_(T)
Russian mathematician
Lie groups produces examples of lattices, called arithmetic lattices. It is analogous to considering the subgroup SL(n,Z) of the real special linear group
Grigory_Margulis
Group in mathematical representation theory
coincides with the special linear group SL2(R). This group biholomorphically acts on the complex upper half-plane by fractional-linear transformations,
Metaplectic_group
even order were shown to be Frobenius groups, abelian groups, or 2-dimensional projective special linear groups over a finite field of even order, PSL(2
CA-group
In projective geometry and linear algebra, the projective orthogonal group PO is the induced action of the orthogonal group of a quadratic space V = (V
Projective_orthogonal_group
Statistical modeling method
In statistics, linear regression is a model that estimates the relationship between a scalar response (dependent variable) and one or more explanatory
Linear_regression
Relativistic quantum mechanical wave equation
the special linear group SL ( 2 , C ) {\displaystyle {\text{SL}}(2,\mathbb {C} )} as its spacetime symmetry group rather than the Lorentz group, since
Dirac_equation
Conjecture on zeros of the zeta function
Ihara in the context of discrete subgroups of the two-by-two p-adic special linear group. A regular finite graph is a Ramanujan graph, a mathematical model
Riemann_hypothesis
Equivalence relation of groups
NG(Γ) (and hence contains Γ). For example, the commensurator of the special linear group SL(n,Z) in SL(n,R) contains SL(n,Q). In particular, the commensurator
Commensurability (group theory)
Commensurability_(group_theory)
Theorem classifying finite simple groups
groups. The most obvious reason is that the list of simple groups is quite complicated: with 26 sporadic groups there are likely to be many special cases
Classification of finite simple groups
Classification_of_finite_simple_groups
Rational function of the form (az + b)/(cz + d)
the complex projective line. They form a group called the Möbius group, which is the projective linear group PGL(2, C). Together with its subgroups, it
Möbius_transformation
Monster and modular connection
expressed in terms of linear combinations of the dimensions of the irreducible representations r n {\displaystyle r_{n}} of the monster group M (sequence A001379
Monstrous_moonshine
only irreducible representations. The Lie algebra sl(2,C) of the special linear group SL(2,C) is the space of 2x2 trace-zero matrices with complex entries
Representation theory of semisimple Lie algebras
Representation_theory_of_semisimple_Lie_algebras
French mathematician (1811–1832)
group of the general equation of degree pν. He constructed the projective special linear group PSL(2,p). Galois constructed them as fractional linear
Évariste_Galois
Commutative group (mathematics)
of linearly independent (over the integers) elements of the group. Finite abelian groups and torsion groups have rank zero, and every abelian group of
Abelian_group
Algebraic structure used in analysis
formula). Here are some matrix Lie groups and their Lie algebras. For a positive integer n, the special linear group S L ( n , R ) {\displaystyle \mathrm
Lie_algebra
SPECIAL LINEAR-GROUP
SPECIAL LINEAR-GROUP
Boy/Male
Hindu
Special
Female
English
Variant spelling of English Linsey, LINSAY means "Lincoln's wetlands."
Girl/Female
Indian, Telugu
Special
Girl/Female
Bengali, Indian, Modern
Special
Girl/Female
Tamil
Special
Girl/Female
Indian
Special
Surname or Lastname
English
English : metronymic from Line.
Girl/Female
Arabic, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Sindhi, Tamil, Telugu
Special
Male
Greek
(ΑἰνÎας) Variant spelling of Greek AineÃas, AINEAS means "praiseworthy."
Girl/Female
Indian
Special
Boy/Male
Hindu
Lingam
Female
Scottish
Variant spelling of Scottish Lilias, LILEAS means "lily."
Girl/Female
Greek, Indian, Marathi, Turkish
Special
Boy/Male
Tamil
Special
Girl/Female
Hindu, Indian, Tamil
Special
Surname or Lastname
English
English : variant of Lingard.French : occupational name for a maker of or dealer in linen goods, from Old French linge ‘linen (goods)’ (see Linge 1).
Boy/Male
Tamil
Saisnigda | ஸாஈஸà¯à®¨à¯€à®•à¯à®¤à®¾
Special
Saisnigda | ஸாஈஸà¯à®¨à¯€à®•à¯à®¤à®¾
Male
English
Irish Anglicized form of Gaelic Fionnbarr, FINBAR means "fair-headed."
Girl/Female
Bengali, Indian, Telugu
Special
Male
Yiddish
 Variant spelling of Yiddish Lieber, LIBER means "beloved." Compare with another form of Liber.
SPECIAL LINEAR-GROUP
SPECIAL LINEAR-GROUP
Girl/Female
Bengali, Hindu, Indian, Tamil
Cute than Anything
Girl/Female
Indian
Beautiful Star; Joyful Noise; Happy Spirit
Girl/Female
Muslim
Bud, Blossom
Boy/Male
Chinese, Finnish, French, German, Polish, Slavic, Swedish
Fame; Glory; Careful; Thoughtful; Glorious Camp or Stand; Glorious Government
Boy/Male
Tamil
Samynathan | ஸமà¯à®¯à®¨à®¾à®¤à®¨
God murugans name (son of Lord Shiva)
Boy/Male
Australian, French, German, Latin, Swiss
From Laurentium; Laurentium was a City South of Rome Known for Its Numerous Laurel Trees; From the Place of the Laurel Trees
Male
Hebrew
(יַעֲשָׂי) Hebrew name YAASUW means "they will do" or "Jehovah made." In the bible, this is the name of a descendant of Bani.
Boy/Male
Hindu, Indian, Modern
Lord Shiva
Boy/Male
English
Friend.
Boy/Male
Arabic, Muslim
The Biblical Lot is the English Language Equivalent; Name of a Prophet
SPECIAL LINEAR-GROUP
SPECIAL LINEAR-GROUP
SPECIAL LINEAR-GROUP
SPECIAL LINEAR-GROUP
SPECIAL LINEAR-GROUP
n.
One appointed for a special service or occasion.
a.
Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf.
a.
Linear.
a.
In the direction of a line; of or pertaining to a line; measured on, or ascertained by, a line; linear; as, lineal magnitude.
a.
Distinguished among others of the same class or kind; special; concerning a species or a single object; principal; particular; as, in an especial manner or degree.
n.
The splenial bone.
a.
Appropriate; designed for a particular purpose, occasion, or person; as, a special act of Parliament or of Congress; a special sermon.
adv.
In a linear manner; with lines.
n.
One who adjusts things to a line or lines or brings them into line.
a.
Of a linear shape.
a.
Composed of lines; delineated; as, lineal designs.
a.
Limited in range; confined to a definite field of action, investigation, or discussion; as, a special dictionary of commercial terms; a special branch of study.
n.
One who lines, as, a liner of shoes.
n.
That for which a person is distinguished, in which he is specially versed, or which he makes an object of special attention; a speciality.
adv.
In a special manner; particularly; especially.
a.
Of or pertaining to a species; constituting a species or sort.
a.
Descending in a direct line from an ancestor; hereditary; derived from ancestors; -- opposed to collateral; as, a lineal descent or a lineal descendant.
a.
Of, pertaining to, or included by, two lines; as, bilinear coordinates.
a.
See Spatial.
a.
Of or pertaining to a line; consisting of lines; in a straight direction; lineal.