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

Abstract

In this paper, we extend the notion of the Brauer–Clifford group to the case of an $(S,\mathcal{G},H)$-comodule algebra, where H is a commutative Hopf algebra, $\mathcal{G}$ 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 $\mathcal{G}$-module algebra and the H-coaction 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.

KEYWORDS AND PHRASES:

• Lie algebras
• Brauer–Clifford groups
• Brauer groups
• Hopf algebras
• Symmetric monoidal categories

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 16K50
• 17B63
• Secondary 16T05