Metabelian Lie and perm algebras
F. A. Mashurov, B. K. Sartayev
TL;DR
This paper demonstrates that all metabelian Lie algebras can be embedded into perm algebras, a special class of associative algebras, and provides a method to construct their universal enveloping perm algebra.
Contribution
It introduces a novel embedding of metabelian Lie algebras into perm algebras and develops a construction method for their universal enveloping perm algebra.
Findings
Metabelian Lie algebras can be embedded into perm algebras.
A method for constructing universal enveloping perm algebras is provided.
The embedding preserves algebraic structures within the perm algebra variety.
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 . In addition, a technical method to construct the universal enveloping perm algebra for a metabelian Lie algebra is given.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology