Some years ago Wilhelm Plesken mentioned to Arjeh Cohen that if G is a group, the elements g – g^-1 span a Lie subalgebra of the group algebra of G. In this talk I shall describe the structure of this algebra when G is a finite group and the group algebra is over the complex numbers. In particular, I will determine for which groups the construction produces a (semi)simple Lie algebra.

This will be a general talk and little knowledge of the theory of Lie algebras is required beyond the definition of a Lie algebra itself and the definitions of simple and semisimple Lie algebras.