Brauer–Clifford Group of ($$\varvec{S,{{\mathcal {G}}},H}$$)-Azumaya Algebras

Abstract

In this paper we extend the notion of the Brauer–Clifford group to the case of an $$(S,{{\mathcal {G}}},H)$$ -algebra, when H is a cocommutative Hopf algebra, $${{\mathcal {G}}}$$ is a Lie algebra in the symmetric monoidal category of left H-modules, and S is a commutative algebra which is an H-module algebra, a $${\mathcal G}$$ -module algebra and the H-action is compatible with the $${\mathcal {G}}$$ -action. This Brauer–Clifford group turns out to be an example of the Brauer group of a symmetric monoidal category.