Metabelian Lie and perm algebras
JOURNAL OF ALGEBRA AND ITS APPLICATIONS(2024)
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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Key words
Perm algebras,Lie and Jordan elements,polynomial identities,Grobner bases
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