On representations of Plesken Lie algebras (Q6650347)

Let \(G\) be a finite group and \(\mathbb{F}G\) the group algebra of \(G\) over the field \(\mathbb{F}\). Then \(\mathbb{F}G\) is also a Lie algebra under the commutator operation. The Lie subalgebra of \(\mathbb{F}G\) generated by \(g-g^{-1}\) for \(g\in G\) is called a Plesken Lie algebra. This paper shows that a representation \(V\) of the group \(G\) yields a representation of the corresponding Plesken Lie algebra. Moreover, the \(V\) is reducible as a representation of the Plesken Lie algebra if the \(G\)-representation \(V\) is reducible.