2022•Journal of Algebra and Its ApplicationsRequires access

Metabelian Lie and perm algebras

Farukh Mashurov, B. K. Sartayev

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 [Formula: see text]. In addition, a technical method to construct the universal enveloping perm algebra for a metabelian Lie algebra is given.

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Key concepts: Mathematics, Universal enveloping algebra, Lie conformal algebra, Non-associative algebra, Pure mathematics, Graded Lie algebra, Algebra over a field, Algebra representation