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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The Brauer group
of Yetter-Drinfel'd module algebras

Authors: S. Caenepeel, F. Van Oystaeyen and Y. H. Zhang
Journal: Trans. Amer. Math. Soc. 349 (1997), 3737-3771
MSC (1991): Primary 16A16, 16A24
MathSciNet review: 1454120
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Abstract: Let $H$ be a Hopf algebra with bijective antipode. In a previous paper, we introduced $H$-Azumaya Yetter-Drinfel'd module algebras, and the Brauer group ${\mathrm {BQ}}(k,H)$ classifying them. We continue our study of ${\mathrm {BQ}}(k,H)$, and we generalize some properties that were previously known for the Brauer-Long group. We also investigate separability properties for $H$-Azumaya algebras, and this leads to the notion of strongly separable $H$-Azumaya algebra, and to a new subgroup of the Brauer group ${\mathrm {BQ}}(k,H)$.

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Additional Information

S. Caenepeel
Affiliation: Faculty of Applied Sciences, Free University of Brussels, VUB, Pleinlaan 2, B-1050 Brussels, Belgium

F. Van Oystaeyen
Affiliation: Department of Mathematics, University of Antwerp, UIA, Universiteitsplein 1, B-2610 Wilrijk, Belgium

Y. H. Zhang

Keywords: Brauer group, Azumaya algebra, Hopf algebra, Yetter-Drinfel\textprime d module, separable algebra
Received by editor(s): August 24, 1994
Received by editor(s) in revised form: March 19, 1996
Additional Notes: The third author wishes to thank the Free University of Brussels for its financial support during the time when this paper was written.
Article copyright: © Copyright 1997 American Mathematical Society