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Metabelian Lie and perm algebras
Published 12 Oct 2021 in math.RA | (2110.06032v2)
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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