The restricted isomorphism problem for metacyclic restricted Lie algebras

Abstract

Let L be a restricted Lie algebra with the restricted enveloping algebra u(L) over a perfect field of positive characteristic p. The restricted isomorphism problem asks what invariants of L are determined by u(L). This problem is the analogue of the modular isomorphism problem for finite p-groups. Baginski and Sandling have given a positive answer to the modular isomorphism problem for metacyclic p-groups. In this paper, we provide a positive answer to the restricted isomorphism problem in case L is metacyclic and p-nilpotent.