On the deformation theory of structure constants for associative algebras

TL;DR

This paper develops an algebraic framework for deforming structure constants of associative algebras using deformation driving algebras, linking these deformations to integrable systems.

Contribution

It introduces a scheme involving zero divisors for deforming associative algebra structure constants and explores their relation to integrable systems.

Findings

Deformation scheme based on zero divisors for associative algebras.

Connection established between algebra deformations and integrable systems.

Analysis of three-dimensional associative algebras with Lie algebra DDAs.

Abstract

Algebraic scheme for constructing deformations of structure constants for associative algebras generated by a deformation driving algebras (DDAs) is discussed. An ideal of left divisors of zero plays a central role in this construction. Deformations of associative three-dimensional algebras with the DDA being a three-dimensional Lie algebra and their connection with integrable systems are studied.