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.
Topics & Concepts
MathematicsUniversal enveloping algebraLie conformal algebraNon-associative algebraPure mathematicsGraded Lie algebraAlgebra over a fieldAlgebra representationLie algebraCellular algebraAffine Lie algebraAssociative algebraAssociative propertyCurrent algebraAdvanced Topics in AlgebraAlgebraic structures and combinatorial modelsHomotopy and Cohomology in Algebraic Topology