Isomorphism invariants of restricted enveloping algebras

2008/04/14 by Hamid Usefi, Usefi, Hamid
Mathematics · #17B35 #17B50 (Primary) #20C05 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0804.2281

openalex publication_date 2008/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L and H be finite-dimensional restricted Lie algebras over a perfect field \F such that u(L)≅ u(H), where u(L) is the restricted enveloping algebra of L. We prove that if L is p-nilpotent and abelian, then L≅ H. We deduce that if L is abelian and \F is algebraically closed, then L≅ H. We use these results to prove the main result of this paper stating that if L is p-nilpotent, then L/L'^p+γ₃(L)≅ H/H'^p+γ₃(H).

Related

• Isomorphism invariants of enveloping algebras
• Lie Properties of Restricted Enveloping Algebras
• Perfect and semiperfect restricted enveloping algebras
• Restricted enveloping algebras whose skew and symmetric elements are Lie\n metabelian
• The isomorphism problem for universal enveloping algebras of nilpotent Lie algebras