Modular Lie representations of groups of prime order (Q1434204)

Let \(K\) be a field of characteristic \(p\) and \(G\) be a group of order \(p\). For a finite-dimensional \(KG\)-module \(V\) and a positive integer \(n\), let \(L^n(V)\) denote the \(n\)-th homogeneous component of the free Lie \(K\)-algebra generated by \(V\) and consider \(L^n(V)\) as a \(KG\)-module. The author gives a formula which describes the module structure of \(L^n(V)\) up to isomorphism.