Brauer-Clifford group of Poisson (S,H)-Hopf algebras - Guédénon, Thomas (Sarajevo Journal of Mathematics, 2024)
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.