Isomorphism invariants of enveloping algebras

2014/11/13 by Hamid Usefi, Usefi, Hamid
Mathematics · #17B30 #17B35 #17B50 #20C05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1411.3734

openalex publication_date 2014/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L be a Lie algebra with its enveloping algebra U(L) over a field. In this paper we survey results concerning the isomorphism problem for enveloping algebras: given another Lie algebra H for which U(L) and U(H) are isomorphic as associative algebras, can we deduce that L and H are isomorphic Lie algebras? Over a field of positive characteristic we consider a similar problem for restricted Lie algebras, that is, given restricted Lie algebras L and H for which their restricted enveloping algebras are isomorphic as algebras, can we deduce that L and H are isomorphic?

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