Skew-symmetric elements of rational group algebras

Abstract

Let RG be the group ring of a finite group G over a commutative ring R with 1. An element x in RG is said to be skew-symmetric with respect to an involution $$\sigma $$ of RG if $$\sigma (x)=-x.$$ A structure theorem for the Lie algebra of skew-symmetric elements of FG is given where F is an algebraic extension of $$\mathbb {Q}$$ which generalizes some previously known results in this direction.