Brauer–Clifford group of -Azumaya comodule algebras

Abstract

In this paper, we extend the notion of the Brauer–Clifford group to the case of an -comodule algebra, where H is a commutative Hopf algebra, is a Lie algebra in the symmetric monoidal category of right H-comodules, and S is a commutative algebra which is an H-comodule algebra, a -module algebra and the H-coaction is compatible with the -action. This Brauer–Clifford group turns out to be an example of the Brauer group of a symmetric monoidal category.