2019/03/16 by José L. Vilca Rodríguez, Rodríguez, José L. Vilca, Csaba Schneider +3
Mathematics · #Advanced Topics in Algebra #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.1903.06915
This paper is a contribution to the isomorphism problem for universal\nenveloping algebras of finite-dimensional Lie algebras. We focus on solvable\nLie algebras of small dimensions over fields of arbitrary characteristic. We\nprove, over an arbitrary field, that the isomorphism type of a metabelian Lie\nalgebra whose derived subalgebra has codimension one is determined by its\nuniversal enveloping algebra. As an application of the results in this paper,\nwe solve the isomorphism problem for solvable Lie algebras of dimension four\nover fields of characteristic zero and also point out the problems that occur\nin prime characteristic.\n