Group algebras of finite groups as Lie algebras

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168092We 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 $G$.12 pagesRepresentation TheoryGroup Theory20C15, 17B99Group algebras of finite groups as Lie algebrastext