  Let G be a finite group. The Plesken Lie algebra L[G] is a subalgebra of the
complex group algebra C[G] and admits a direct-sum decomposition into simple
Lie algebras based on the ordinary character theory of G. In this paper we
review the known results on L[G] and related Lie algebras, as well as introduce
a conjecture on a characteristic p analog L_p[G], with a focus on when p
divides the order of G.
