Metabelian Lie and perm algebras

2021/10/12 by Mashurov, F. A., Sartayev, B. K. · 2 citations
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2110.06032

Abstract

It is well known that any Lie algebra can be embedded into an associative algebra. We prove that any metabelian Lie algebra can be embedded into an algebra in the subvariety of perm algebras, i.e., associative algebras with the identity abc-acb =0. In addition, a technical method to construct the universal enveloping perm algebra for a metabelian Lie algebra is given.

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• Free Algebras in Mal'cev-Type Subvarieties of Associative Algebras
• 4-type subvarieties of the variety of associative algebras

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