Noncommutative Algebra and Representation Theory: Symmetry, Structure & Invariants

Abstract

This is an abridged version of our Habilitation thesis. In these notes, we aim to summarize our research interests and achievements as well as motivate what drives our work: symmetry, structure and invariants. The paradigmatic example which permeates and often inspires our research is the Weyl algebra $\mathbb{A}_{1}$.