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searching for Semisimple algebra 8 found (21 total)

Associative algebra (4,449 words) [view diff] exact match in snippet view article find links to article

and Quillen, is a sort of generalization of a free algebra and a semisimple algebra over an algebraically closed field. The universal enveloping algebra

Affine Lie algebra (2,467 words) [view diff] exact match in snippet view article find links to article

simple components of the semisimple algebra. In physics, one often considers instead the direct sum of a semisimple algebra and an abelian algebra C n

Cartan's criterion (794 words) [view diff] exact match in snippet view article find links to article

it follows easily from Cartan's criterion for solvability that a semisimple algebra (in characteristic 0) has a non-degenerate Killing form. Cartan's

Free Lie algebra (1,272 words) [view diff] exact match in snippet view article find links to article

on a semisimple Lie algebra uses a free Lie algebra to construct a semisimple algebra out of generators and relations. The Milnor invariants of a link group

Abstract algebra (4,175 words) [view diff] exact match in snippet view article find links to article

uniquely decomposes into the direct sums of a nilpotent algebra and a semisimple algebra that is the product of some number of simple algebras, square matrices

Lie algebra representation (4,308 words) [view diff] exact match in snippet view article find links to article

reductive Lie algebra is a direct sum of a commutative algebra and a semisimple algebra. An element v of V is said to be g {\displaystyle {\mathfrak {g}}}

Semisimple Lie algebra (5,731 words) [view diff] exact match in snippet view article find links to article

is the semidirect product of a solvable ideal (its radical) and a semisimple algebra. In particular, there is no nonzero Lie algebra that is both solvable

Representation theory of finite groups (21,307 words) [view diff] exact match in snippet view article find links to article

representations. This is analogous to the corresponding definition for a semisimple algebra. For the definition of the direct sum of representations please refer