Extensions of associative and Lie algebras via Gröbner-Shirshov bases method

Abstract

Let a, b, e be algebras over a field k. Then e is an extension of a by b if a is an ideal of e and b is isomorphic to the quotient algebra e/a. In this paper, by using Gröbner-Shirshov bases theory for associative (resp. Lie) algebras, we give complete characterizations of associative (resp. Lie) algebra extensions of a by b, where b is presented by generators and relations.

Gröbner-Shirshov bases theory and extensions of Leibniz superalgebras

“…There are many results on extensions of algebras, in particular, on extensions of associative algebras, Lie (super)algebras, Leibniz (super)algebras, etc, see, for example, [4,5,20,21,24,29,35]. Mostly, they deal with some special cases for extensions.…”