Research Seminar in Mathematics - Theory of non-commutative and non-associative polynomial rings

Speaker

Per Bäck, Mälardalen University.

Abstract

In this talk, I will give an introduction to the theory of non-commutative polynomial rings known as Ore extensions, and then show how this can be generalized to the non-associative setting. In particular, I will discuss hom-associative Ore extensions and how they provide a framework for deforming otherwise rigid algebras appearing in e.g. quantum physics, such as the Weyl algebras. I will also show how these deformations induce deformations of the corresponding commutator Lie algebras into so-called hom-Lie algebras.

In the end, we will see how the classical Hilbert’s basis theorem for commutative polynomial rings can be extended to a non-commutative and non-associative version, and applications thereof including quaternionic and octonionic rings.