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 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.
Keywords: Hopf algebras, Yetter-Drinfel'd modules, Braided monoidal categories, Brauer groups
2010 MSC: Primary: 16W30; Secondary: 16K50, 16T05,18D10
Theory and Applications of Categories, Vol. 33, 2018, No. 9, pp 216-252.