Isomorphism invariants of restricted enveloping algebras

Hamid Usefi

Vol. 246 (2010), No. 2, 487–494

DOI: 10.2140/pjm.2010.246.487

Abstract

Let L and H be finite-dimensional restricted Lie algebras over a perfect field 𝔽. Suppose u(L)≅u(H), where u(L) is the restricted enveloping algebra of L. We prove that L≅H if L is p-nilpotent and abelian, or if L is abelian and 𝔽 is algebraically closed. We use these results to prove our main result, that if L is p-nilpotent, then L∕L′^p + γ₃(L)≅H∕H′^p + γ₃(H).

Keywords

restricted Lie algebras, enveloping algebras, isomorphism problem

Mathematical Subject Classification 2000

Primary: 17B35, 17B50

Secondary: 20C05

Milestones

Received: 7 April 2009

Revised: 17 December 2009

Accepted: 21 December 2009

Published: 1 June 2010