representation theory, the Levi decomposition, conjectured by Wilhelm Killing and Élie Cartan and proved by Eugenio Elia Levi (1905), states that any finite-dimensional...

Jordan–Chevalley decomposition of an element in algebraic group as a product of semisimple and unipotent elements The Bruhat decomposition G = B W B {\displaystyle...

{\mathfrak {a}},} while if the radical equals the center the Levi decomposition yields a decomposition g = s 0 ⊕ z ( g ) . {\displaystyle {\mathfrak {g}}={\mathfrak...

two large and generally complementary classes, as is shown by the Levi decomposition. The solvable Lie algebras are precisely those that can be obtained...

in g {\displaystyle {\mathfrak {g}}} ). This is in contrast to the Levi decomposition: the short exact sequence 0 → r a d ( g ) → g → g s s → 0 {\displaystyle...

semidirect product of a solvable Lie group and a semisimple Lie group (the Levi decomposition). The classification of representations of solvable Lie groups is...

three papers in group theory: in the first one, Levi (1905) discovered what is now called Levi decomposition, which was conjectured by Wilhelm Killing and...

field or rotation field. This decomposition does not exist for all vector fields and is not unique. The Helmholtz decomposition in three dimensions was first...

Killing horizon Killing spinor Killing tensor Killing vector field Levi decomposition G2 (mathematics) Root system O'Conner, J. J.; Robertson, E. F. (February...

{\displaystyle K({\mathfrak {g}},[{\mathfrak {g}},{\mathfrak {g}}])=0.} The Levi decomposition asserts that every finite-dimensional Lie algebra over a field of...

Lie algebras include Whitehead's lemmas, Weyl's theorem, and the Levi decomposition theorem. Let g {\displaystyle {\mathfrak {g}}} be a Lie algebra over...

simply connected) and their compactness. A first key result is the Levi decomposition, which says that every simply connected Lie group is the semidirect...

algebra is reductive if and only if its radical equals its center. Levi decomposition Hazewinkel, Michiel; Gubareni, Nadiya; Kirichenko, V. V. (2010), Algebras...

is zero. The significance of semisimplicity comes firstly from the Levi decomposition, which states that every finite dimensional Lie algebra is the semidirect...

R\to 1.} If k has characteristic zero, then one has the more precise Levi decomposition: every connected linear algebraic group G over k is a semidirect product...

technical methods were available, often inductive in nature and based on Levi decompositions amongst other matters, but the field remained demanding. From the...

decomposition or rank-R decomposition is the decomposition of a tensor as a sum of R rank-1 tensors, where R is minimal. Computing this decomposition...

Paul Levi (German: [ˈleːvi]; 11 March 1883 – 9 February 1930) was a German communist and social democratic political leader. He was the head of the Communist...

defined from its decomposition into the product of transpositions as sgn(σ) = (−1)m where m is the number of transpositions in the decomposition. Although such...

Jordan–Chevalley decomposition also exist for elements of Linear algebraic groups and Lie groups via a multiplicative reformulation. The decomposition is an important...

possessing some kind of symmetry. Important examples include: holonomy of the Levi-Civita connection in Riemannian geometry (called Riemannian holonomy), holonomy...

group that is invariant under inner automorphisms. Iwasawa decomposition Iwasawa decomposition Jacobi identity 1.   Carl Gustav Jacob Jacobi (1804 – 1851)...

famous as the discoverer of tensor calculus. With his former student Tullio Levi-Civita, he wrote his most famous single publication, a pioneering work on...

write in the language we inherit. Discussing the anthropology of Claude Lévi-Strauss, Derrida argues that we are all bricoleurs, creative thinkers who...

{\displaystyle c} . This is a solution to the so-called Levi problem, named after Eugenio Levi (1911). The function ψ {\displaystyle \psi } invites a generalization...

particular Theorems 18 (relating ear decomposition to circuit rank) and 19 (on the existence of ear decompositions). Brualdi, Richard A. (2006), Combinatorial...

for which such a decomposition is possible is the symmetric rank of T. This minimal decomposition is called a Waring decomposition; it is a symmetric...

theory of quantum gravity. The term was introduced in this sense by Robert Lévi in 1927. A quantum theory in which time is a quantum variable with a discrete...

curvature tensor can be decomposed into a Weyl part and a Ricci part. This decomposition is known as the Ricci decomposition, and plays an important role...

Gradient Divergence Curl Laplacian Directional derivative Identities Theorems Gradient Green's Stokes' Divergence generalized Stokes Helmholtz decomposition...