Metabelian Lie and perm algebras
Mashurov F.A. Sartayev B.K.
1 March 2024World Scientific
Journal of Algebra and its Applications
2024#23Issue 4
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.
Gröbner bases , Lie and Jordan elements , Perm algebras , polynomial identities
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Suleyman Demirel University, Kaskelen, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Sobolev Institute of Mathematics, Novosibirsk, Russian Federation
Suleyman Demirel University
Institute of Mathematics and Mathematical Modeling
Sobolev Institute of Mathematics
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