Abstract
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.
ACKNOWLEDGMENTS
It is my pleasure to thank J. Vargas and O. Glass for useful discussions and references about harmonic analysis.
Notes
Communicated by J. Alev.