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German mathematician (1847–1923)
Wilhelm Karl Joseph Killing (10 May 1847 – 11 February 1923) was a German mathematician who made important contributions to the theories of Lie algebras
Wilhelm_Killing
Symmetric bilinear form in mathematics
In mathematics, the Killing form, named after Wilhelm Killing, is a symmetric bilinear form that plays a basic role in the theories of Lie groups and
Killing_form
Vector field on a pseudo-Riemannian manifold that preserves the metric tensor
In mathematics and theoretical physics, a Killing vector field or Killing field (named after Wilhelm Killing) is a vector field on a Riemannian manifold
Killing_vector_field
Connected non-abelian Lie group lacking nontrivial connected normal subgroups
groups was by Wilhelm Killing, and this work was later perfected by Élie Cartan. The final classification is often referred to as Killing-Cartan classification
Simple_Lie_group
Matrices named after Élie Cartan
in the context of Lie algebras were first investigated by Wilhelm Killing, whereas the Killing form is due to Cartan.[citation needed] A (symmetrizable)
Cartan_matrix
Surname list
(1959–2019), French actress Wesley Killing (born 1993), Canadian pair skater Wilhelm Killing (1847–1923), German mathematician Killings (surname) This page lists
Killing_(surname)
Tensor in general relativity
generally lack such a direct geometric interpretation. Killing tensors are named after Wilhelm Killing. In the following definition, parentheses around tensor
Killing_tensor
Topics referred to by the same term
concepts named after Wilhelm Killing: Killing tensor, a generalization of a Killing vector field Killing vector field or Killing field, a vector field
Killing
Geometrical construct in general relativity
Mathematically a Killing horizon is a null hypersurface defined by the vanishing of the norm of a Killing vector field (both are named after Wilhelm Killing). It
Killing_horizon
Mathematical method to analyse Lie groups
and representation theory, the Levi decomposition, conjectured by Wilhelm Killing and Élie Cartan and proved by Eugenio Elia Levi (1905), states that
Levi_decomposition
Vector field in conformal geometry
The name Killing refers to Wilhelm Killing, who first investigated Killing vector fields. A vector field X {\displaystyle X} is a Killing vector field
Conformal Killing vector field
Conformal_Killing_vector_field
German mathematician (1815–1897)
Karl Theodor Wilhelm Weierstrass (/ˈvaɪərˌstrɑːs, -ˌʃtrɑːs/; German: Weierstraß [ˈvaɪɐʃtʁaːs]; 31 October 1815 – 19 February 1897) was a German mathematician
Karl_Weierstrass
Study of Lie groups, Lie algebras and differential equations
groups, which is one of the areas of mathematics, and was worked out by Wilhelm Killing and Élie Cartan. The foundation of Lie theory is the exponential map
Lie_theory
Generalized matrix decomposition for Lie groups and Lie algebras
matrices. Its history can be traced to the 1880s work of Élie Cartan and Wilhelm Killing. Let g {\displaystyle {\mathfrak {g}}} be a real semisimple Lie algebra
Cartan_decomposition
Concept in Lie algebra mathematics
classification of real simple Lie algebras is one of the major achievements of Wilhelm Killing and Élie Cartan. Over a field of characteristic 0, a direct sum of
Simple_Lie_algebra
German Emperor from 1888 to 1918
Wilhelm II (Friedrich Wilhelm Viktor Albert; 27 January 1859 – 4 June 1941) was the last German Emperor from 1888 until his abdication in 1918. His fall
Wilhelm_II
Type of Dirac operator eigenspinor
after Wilhelm Killing. Another equivalent definition is that Killing spinors are the solutions to the Killing equation for a so-called Killing number
Killing_spinor
Geometric arrangements of points, foundational to Lie theory
theory.) The concept of a root system was originally introduced by Wilhelm Killing around 1889 (in German, Wurzelsystem). He used them in his attempt
Root_system
Theorem in Lie representation theory
mathematician Friedrich Engel, who sketched a proof of it in a letter to Wilhelm Killing dated 20 July 1890 (Hawkins 2000, p. 176). Engel's student K.A. Umlauf
Engel's_theorem
Simple Lie group; the automorphism group of the octonions
discovered in the attempt to classify simple Lie algebras. On May 23, 1887, Wilhelm Killing wrote a letter to Friedrich Engel saying that he had found a 14-dimensional
G2_(mathematics)
French mathematician (1869–1951)
subject of classification of simple Lie groups, which was started by Wilhelm Killing. In 1892 Lie came to Paris, at the invitation of Darboux and Tannery
Élie_Cartan
Subgroup of the group of invertible n×n matrices
simple Lie group SL(n,R).) The simple Lie groups were classified by Wilhelm Killing and Élie Cartan in the 1880s and 1890s. At that time, no special use
Linear_algebraic_group
248-dimensional exceptional simple Lie group
eight peaks related to E8 that were predicted by Zamolodchikov (1989). Wilhelm Killing (1888a, 1888b, 1889, 1890) discovered the complex Lie algebra E8 during
E8_(mathematics)
Algebraic structure used in analysis
transformations by Sophus Lie in the 1870s, and independently discovered by Wilhelm Killing in the 1880s. The name Lie algebra was given by Hermann Weyl in the
Lie_algebra
Relation used in geometry
parallel lines on the primitive notion of direction. According to Wilhelm Killing the idea may be traced back to Leibniz. Wilson, without defining direction
Parallel_(geometry)
German mathematician and physicist (1864–1909)
related to Lorentz transformations, which included contributions of Wilhelm Killing (1880, 1885), Henri Poincaré (1881), Homersham Cox (1881), Alexander
Hermann_Minkowski
Invariance of operations under geometric translation
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Translational_symmetry
German military transport ship which sank in 1945; former cruise ship
MV Wilhelm Gustloff was a German military transport ship, which was taking part in Operation Hannibal, when it was sunk by Soviet submarine S-13 in the
MV_Wilhelm_Gustloff
Group that is also a differentiable manifold with group operations that are smooth
profound influence on subsequent development of mathematics, was made by Wilhelm Killing, who in 1888 published the first paper in a series entitled Die Zusammensetzung
Lie_group
Group of unitary complex matrices with determinant of 1
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Special_unitary_group
Type of subgroup of an algebraic group
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Borel_subgroup
Mathematical group
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Symplectic_group
Russian mathematics award
Kazan State University's Lobachevsky Medal. 1897 - Sophus Lie 1900 - Wilhelm Killing 1903 - David Hilbert 1909 - Ludwig Schlesinger (awarded in 1912) 1912
Lobachevsky_Prize
German field marshal and war criminal (1882–1946)
Wilhelm Bodewin Johann Gustav Keitel (German pronunciation: [ˈvɪlhɛlm ˈkaɪtl̩]; 22 September 1882 – 16 October 1946) was a German field marshal who held
Wilhelm_Keitel
Alfred J. Lotka and Vito Volterra Conformal Killing equation Topology, Differential geometry Wilhelm Killing Darcy–Weisbach equation Fluid dynamics Henry
List of scientific equations named after people
List_of_scientific_equations_named_after_people
Type of non-Euclidean geometry
This model is generally credited to Poincaré, but Reynolds says that Wilhelm Killing used this model in 1885. This model has direct application to special
Hyperbolic_geometry
medical chemistry Paul Kevenhörster (born 1941), Political scientist Wilhelm Killing (1847–1923), mathematician Paul Kirchhof (born 1943), jurist Johann
List of University of Münster people
List_of_University_of_Münster_people
recorders of folk and fairy tales Deutsche Mark DM 1,000 obverse 1992–2002 Wilhelm Grimm 1786–1859 younger of the Brothers Grimm, recorders of folk and fairy
List_of_people_on_banknotes
Lie algebra over the field of real numbers. By Cartan's criterion, the Killing form is nondegenerate, and can be diagonalized in a suitable basis with
Real_form_(Lie_theory)
German mathematician (1810–1893)
Doctoral students Gotthold Eisenstein Georg Frobenius Lazarus Fuchs Wilhelm Killing Adolf Kneser Franz Mertens Hermann Schwarz Georg Cantor Hans Carl Friedrich
Ernst_Kummer
Mathematical transformation in physics
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Time-translation_symmetry
Root system associated to a symmetric space
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Restricted_root_system
Branch of mathematics that studies abstract algebraic structures
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Representation_theory
Direct sum of simple Lie algebras
semisimple Lie algebras over the complex numbers were first classified by Wilhelm Killing (1888–90), though his proof lacked rigor. His proof was made rigorous
Semisimple_Lie_algebra
Subgroup of a root system's isometry group
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Weyl_group
Term in mathematics
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Satake_diagram
Needs Of Students Of Applied Mathematics, Ginn and Company Following Wilhelm Killing (1885) and others, Woods described motions in spaces of non-Euclidean
Frederick_S._Woods
52-dimensional exceptional simple Lie group
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
F4_(mathematics)
Kac–Moody algebra Kac–Moody algebra Killing 1. Wilhelm Killing (1847 – 1923), a German mathematician. 2. The Killing form on a Lie algebra g {\displaystyle
Glossary of Lie groups and Lie algebras
Glossary_of_Lie_groups_and_Lie_algebras
Canadian mathematician
what was to become Kac–Moody algebra. Kac and Moody noticed that if Wilhelm Killing's conditions were relaxed, it was still possible to associate to the
Robert_Moody
Lie algebra, usually infinite-dimensional
in a similar fashion. The initial construction by Élie Cartan and Wilhelm Killing of finite dimensional simple Lie algebras from the Cartan integers
Kac–Moody_algebra
Austrian psychoanalyst (1897–1957)
Wilhelm Reich (/raɪx/; Austrian German: [ˈvɪlhɛlm ˈraɪç]; 24 March 1897 – 3 November 1957) was an Austrian doctor of medicine and a psychoanalyst, a member
Wilhelm_Reich
Group of 𝑛 × 𝑛 invertible matrices
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
General_linear_group
Group of flat spacetime symmetries
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Poincaré_group
Group without normal subgroups other than the trivial group and itself
Dickson, following the classification of complex simple Lie algebras by Wilhelm Killing. Dickson also constructed exception groups of type G2 and E6 as well
Simple_group
Group of unitary matrices
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Unitary_group
discovered the first one in 1910. Cartan matrices, first investigated by Wilhelm Killing. Cardano's formula, the solution to general cubic equations. Cardano
List of examples of Stigler's law
List_of_examples_of_Stigler's_law
Model of n-dimensional hyperbolic geometry
to the Euclidean group E(n−1). In several papers between 1878–1885, Wilhelm Killing used the representation he attributed to Karl Weierstrass for Lobachevskian
Hyperboloid_model
Pictorial representation of symmetry
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Dynkin_diagram
133-dimensional exceptional simple Lie group
root lattice, which has rank 7. The designation E7 comes from the Cartan–Killing classification of the complex simple Lie algebras, which fall into four
E7_(mathematics)
Feature of a system that is preserved under some transformation
are Killing vector fields which are those spacetime symmetries that preserve the underlying metric structure of a manifold. In rough terms, Killing vector
Symmetry_(physics)
Concept in mathematics
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Special_linear_Lie_algebra
Group representation
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Representation_of_a_Lie_group
In mathematics, a type of algebra
{\displaystyle {\mathfrak {g}}_{i}/{\mathfrak {g}}_{i+1}} is abelian. (vii) The Killing form B {\displaystyle B} of g {\displaystyle {\mathfrak {g}}} satisfies
Solvable_Lie_algebra
Group of matrices with determinant 1
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Special_linear_group
78-dimensional exceptional simple Lie group
root lattice, which has rank 6. The designation E6 comes from the Cartan–Killing classification of the complex simple Lie algebras (see Élie Cartan § Work)
E6_(mathematics)
2007 book by Ian Stewart
Bookworm Marius Sophus Lie formalized Lie groups and Lie algebras. Wilhelm Killing classified all simple Lie algebras (in what Ian Stewart calls the "greatest
Why_Beauty_Is_Truth
Representation theory of an important group in physics
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Representation theory of the Poincaré group
Representation_theory_of_the_Poincaré_group
Mathematical term
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Adjoint_representation
Isometry group of Euclidean space
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Euclidean_group
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Index_of_a_Lie_algebra
Manifold with inversion symmetry
with H acting by isometries. A canonical example is given by minus the Killing form. Under such an inner product, k {\displaystyle {\mathfrak {k}}} and
Hermitian_symmetric_space
Lie groups and their associated Lie algebras
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Table_of_Lie_groups
President of East Germany from 1949 to 1960
Friedrich Wilhelm Reinhold Pieck (German pronunciation: [ˈvɪlhɛlm ˈpiːk]; 3 January 1876 – 7 September 1960) was a German communist politician who served
Wilhelm_Pieck
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Split_Lie_algebra
criterion, the Killing form is non-degenerate if and only if the Lie algebra is semisimple. If g is in addition a simple Lie algebra, then the Killing form is
Quadratic_Lie_algebra
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Lie_point_symmetry
History of a branch of mathematics
started systematically in 1884 with Sophus Lie, followed by work of Wilhelm Killing, Eduard Study, Issai Schur, Ludwig Maurer, and Élie Cartan. The discontinuous
History_of_group_theory
German SS commander (1911–2001)
Wilhelm Mohnke (15 March 1911 – 6 August 2001) was a German brigadier general who was one of the original members of the Schutzstaffel SS-Stabswache Berlin
Wilhelm_Mohnke
German admiral (1887–1945)
Wilhelm Franz Canaris (1 January 1887 – 9 April 1945) was a German admiral and the chief of the Abwehr (the German military-intelligence service) from
Wilhelm_Canaris
Nilpotent subalgebra of a Lie algebra
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Cartan_subalgebra
Dunkl operator Modular form Langlands program Sophus Lie (1842 – 1899) Wilhelm Killing (1847 – 1923) Élie Cartan (1869 – 1951) Hermann Weyl (1885 – 1955)
List_of_Lie_groups_topics
Construction in group theory
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Projective_linear_group
Representation of the symmetry group of spacetime in special relativity
classification of simple Lie algebras was essentially completed by Wilhelm Killing. In 1913 the theorem of highest weight for representations of simple
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
(pseudo-)Riemannian manifold whose geodesics are reversible
(\operatorname {ad} X\circ \operatorname {ad} Y)} is the Killing form. The minus sign appears because the Killing form is negative-definite on h ; {\displaystyle
Symmetric_space
Characterizes complete connected Riemannian manifolds of constant curvature
Mathematische Annalen, 95 (1): 313–339, doi:10.1007/BF01206614, ISSN 0025-5831 Killing, Wilhelm (1891), "Ueber die Clifford-Klein'schen Raumformen", Mathematische
Killing–Hopf_theorem
local geometry may be tied to spaces that are globally different". Wilhelm Killing thought that for free mobility of rigid bodies there are four spaces:
Clifford–Klein_form
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Representation theory of semisimple Lie algebras
Representation_theory_of_semisimple_Lie_algebras
Mathematical theory
Intrinsically and algebraically, a compact Lie algebra is a real Lie algebra whose Killing form is negative definite; this definition is more restrictive and excludes
Compact_Lie_algebra
Group that is a topological space with continuous group operations
equivalence. Finally, compact connected Lie groups have been classified by Wilhelm Killing, Élie Cartan, and Hermann Weyl. As a result, there is an essentially
Topological_group
Branch of mathematics
all elements of g {\displaystyle {\mathfrak {g}}} are ad-nilpotent. The Killing form of a nilpotent Lie algebra is 0. A nonzero nilpotent Lie algebra has
Nilpotent_Lie_algebra
Group theory theorem
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Closed-subgroup_theorem
Universal construction of a complex Lie group from a real Lie group
) ) , {\displaystyle \displaystyle {(X,Y)=-B(X,c(Y)),}} where B is the Killing form on g C {\displaystyle {\mathfrak {g}}_{\mathbf {C} }} . Thus ψ2 is
Complexification_(Lie_group)
German Nazi Party politician (1877–1946)
Wilhelm Frick (12 March 1877 – 16 October 1946) was a German politician of the Nazi Party (NSDAP) and convicted war criminal. He served as Minister of
Wilhelm_Frick
Representation theory of the symmetries of non-relativistic quantum space
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Representation theory of the Galilean group
Representation_theory_of_the_Galilean_group
Mathematical group of loops in a Lie group
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Loop_group
German field marshal (1880–1971)
Siegmund Wilhelm Walther List (14 May 1880 – 17 August 1971) was a German war criminal and Generalfeldmarschall (Field Marshal) of the Wehrmacht during
Wilhelm_List
Grisebach Andreas Müller, Ilka Welz, Anett Dornbusch Drama Loving and Killing Wolf Gremm Anne Brendler [de], Gesine Cukrowski, Bernhard Schir [de], Francis
List of German films of the 2000s
List_of_German_films_of_the_2000s
Representation of a Lie algebra as a set of linear transformations
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Lie_algebra_representation
Physics-mathematics connection
Galilean group representations Scientists Sophus Lie Henri Poincaré Wilhelm Killing Élie Cartan Hermann Weyl Claude Chevalley Harish-Chandra Armand Borel
Particle physics and representation theory
Particle_physics_and_representation_theory
travel, tourism, insurance
WILHELM KILLING
WILHELM KILLING
Male
Scandinavian
Scandinavian form of Old Norse Vilhjalmr, VILHELM means "will-helmet."
Boy/Male
Danish Teutonic Swedish
Boy/Male
German, Polish
Helmet Protection; Will Desire
Male
German
Contracted form of Old High German Willahelm, WILHELM means "will-helmet."Â
Male
German
Latin form of Old High German Wilhelm, WILHELMUS means "will-helmet."
Boy/Male
Teutonic
Resolute defender.
Girl/Female
Danish, Finnish, German
Will; Desire; Helmet
Boy/Male
British, English
From the Bend in the Road
Female
Irish
Feminine form of Irish Gaelic Féidhlim, possibly FÉIDHELM means "hospitable." In Irish legend, this was the name of a daughter of Conchobhar.
Boy/Male
Finnish, German, Swedish, Teutonic
Will-helmet; Desire; Will; Bright; Famous
Female
Scandinavian
Feminine form of Scandinavian Vilhelm, VILHELMA means "will-helmet."
Male
French
Norman French form of Old High German Wilhelm, WILLELM means "will-helmet."
Boy/Male
Australian, Dutch, Teutonic
Strong Helmet; Will Helmet; Protect
Male
Finnish
Finnish form of German Wilhelm, VILHELMI means "will-helmet."
Male
Esperanto
Esperanto form of German Wilhelm, VILHELMO means "will-helmet."
Boy/Male
Teutonic
Strong helmet.
Boy/Male
Australian, Danish, Dutch, Finnish, French, German, Polish, Swedish, Swiss, Teutonic
German Form of William; Will-helmet; Will Desire; Helmet Protection
Boy/Male
German American Teutonic
Surname or Lastname
English
English : variant spelling of Witham.
Male
Swiss
, resolute helmet.
WILHELM KILLING
WILHELM KILLING
WILHELM KILLING
WILHELM KILLING
WILHELM KILLING
WILHELM KILLING
WILHELM KILLING
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