Azumaya skew group algebras and an application to quantum Kleinian singularities
Rings and Algebras
2017-11-28 v2
Abstract
We provide easily-verified necessary and sufficient conditions for a skew group ring, or more generally, a crossed product ring, to be an Azumaya algebra. We use our results to show that (suitable localisations of) skew group rings associated to the quantum Kleinian singularities introduced by Chan, Kirkman, Walton, and Zhang in [CKWZ16a] are Azumaya, and use this to show that these algebras are maximal orders. We also give a new proof of Auslander's Theorem for quantum Kleinian singularities.
Keywords
Cite
@article{arxiv.1711.08669,
title = {Azumaya skew group algebras and an application to quantum Kleinian singularities},
author = {Simon Crawford},
journal= {arXiv preprint arXiv:1711.08669},
year = {2017}
}
Comments
26 pages. Removed table of contents due to it causing a formatting error later in the paper