On constructing deformations of noncommutative algebras

TL;DR

This paper introduces new methods for constructing flat deformations of associative algebras, generalizing previous techniques and providing solutions for specific algebraic deformation problems.

Contribution

It presents a generalized deformation construction method and a new approach for deforming from N to a semisimple algebra A, extending existing frameworks.

Findings

Deformation methods are applicable to polynomial type algebras.

A new method for deforming from N to A is introduced.

The paper answers a specific question on deformations of Acons.

Abstract

This paper presents a method for constructing flat deformations of associative algebras. We will refer to this method as method two because it is a generalisation of the method obtained in [1]. The deformations obtained using the first two methods are of polynomial type. We also present a third method, for the construction of deformations from N to A, for a semisimple algebra A. As an applied example, we answer a question posed by Michael Wemyss on deformations of Acons.