Group algebras of finite groups as Lie algebras

Details Group algebras of finite groups as Lie algebras Group algebras of finite groups as Lie algebras

2008-08-30

arxiv.org/abs/0809.0074v1

Mathematics

Representation Theory

12 pages

Scientific paper

We consider the natural Lie algebra structure on the (associative) group
algebra of a finite group $G$, and show that the Lie subalgebras associated to
natural involutive antiautomorphisms of this group algebra are reductive ones.
We give a decomposition in simple factors of these Lie algebras, in terms of
the ordinary representations of $G$.

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