Brauer-Clifford group of Poisson $(S,H)$-Hopf algebras

Abstract

In this paper, we extend the notion of the Brauer-Clifford group to the case of an Azumaya-Poisson $(S,H)$-Hopf algebra, when $H$ is a commutative Hopf algebra and $S$ is an $H$-comodule Poisson algebra. This is the situation that arises in applications with connections to algebraic geometry. We give three useful examples : an affine algebraic group acting rationally on a Poisson algebra, a Hopf algebra coacting on the localization of a Poisson algebra and a direct product of Hopf algebras coacting on a direct product of Poisson algebras.