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

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Thomas Guedenon and Allen Herman

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.

Published 2018-03-15.

http://www.tac.mta.ca/tac/volumes/33/9/33-09.pdf

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