Unified computational approach to nilpotent algebra classification problems

Abstract

In this article, we provide an algorithm with Wolfram Mathematica code that gives a unified computational power in classification of finite dimensional nilpotent algebras using Skjelbred-Sund method. To illustrate the code, we obtain new finite dimensional Moufang algebras.

The algebraic and geometric classification of nilpotent binary and mono Leibniz algebras

“…The algebraic classification (up to isomorphism) of algebras of dimension n from a certain variety defined by a certain family of polynomial identities is a classic problem in the theory of non-associative algebras. There are many results related to the algebraic classification of small-dimensional algebras in the varieties of Jordan, Lie, Leibniz, Zinbiel, and many other algebras [2,5,6,29,38] and references in [30,36]. Geometric properties of a variety of algebras defined by a family of polynomial identities have been an object of study since 1970's (see, [5,6,13,16,21,22,28,31,33,49] and references in [30]).…”

Unified computational approach to nilpotent algebra classification problems

“…In the follow up section § 3 we provide new results to illustrate our unified symbolic computational approach. The original code by the authors is provided open access through (Kadyrov and Mashurov, 2020). Finally in § 4 we conclude with possible future research directions.…”