Brauer–Clifford group of Azumaya–Poisson (S, H)-algebras

Abstract

In this paper we extend the notion of the Brauer–Clifford group to the case of an Azumaya–Poisson (S, H)-algebra, when H is a cocommutative Hopf algebra and S is an H-module Poisson algebra. This is the situation that arises in applications with connections to differential geometry, algebraic geometry and quantum groups. These Brauer–Clifford groups turn out to be an example of the Brauer group of a symmetric monoidal category.