## A Brauer-Clifford-long group for the category of dyslectic Hopf Yetter-Drinfel'd $(S,H)$-module algebras

### Summary

Brauer-Clifford groups are equivariant Brauer groups for which a Hopf algebra acts or coacts nontrivially on the base ring. Brauer-Clifford groups have been established previously in the category of modules for a skew group ring $S\#G$, the category of modules for the smash product $S\#H$ over a cocommutative Hopf algebra $H$, and its dual category of ($S,H$)-Hopf modules $_S\Cal M^H$ over a commutative Hopf algebra $H$. In this article the authors introduce a Brauer-Clifford group for the category of dyslectic Hopf Yetter-Drinfel'd ($S,H$)-modules for an $H$-commutative base ring $S$ and quantum group $H$. This is the first such example in a category of modules for a quantum group, and it gives a new example of an equivariant Brauer group in a braided monoidal category.

### Mathematics Subject Classification

16W30, 16K50, 16T05, 18D10

### Keywords/Phrases

Hopf algebras, Yetter-Drinfel'd modules, braided monoidal categories, Brauer groups