Azumaya Skew Group Algebras and Quantum Kleinian Singularities

Simon Crawford (Edinburgh)

Frank Adams 1,

In this talk, I will give a simple geometric criterion to determine when a skew group ring is Azumaya. Unlike a number of other results in the literature, this criterion is easy to check in concrete examples, as I will demonstrate. I will then outline how this result can be used to show that quantum Kleinian singularities, as defined by Chan-Kirkman-Walton-Zhang, are maximal orders. This allows for an alternative proof of Auslander's Theorem for these singularities.

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