Noncommutative algebra and representation theory: symmetry, structure \& invariants (Q6591999)

This is an abridged version of фгерщкы Habilitation thesis. In these notes, he aims to summarize his research interests and achievements as well as motivate what drives his work: symmetry, structure and invariants. The paradigmatic example which permeates and often inspires our research is the Weyl algebra \({\mathbb A}_1\).\N\NSpecific of this nicely written and important review is to consider together with Weil algebra its relatives such as universal enveloping algebras of different types and quantum algebras and their deformations. I reccommend to look [\textit{A. Belov-Kanel} and \textit{M. Kontsevich}, Lett. Math. Phys. 74, No. 2, 181--199 (2005; Zbl 1081.16031); \textit{M. Kontsevich}, Jpn. J. Math. (3) 4, No. 1, 1--25 (2009; Zbl 1215.14014)].