Transactions of the American Mathematical Society

Author(s): S. Caenepeel; F. Van Oystaeyen; Y. H. Zhang
Journal: Trans. Amer. Math. Soc. 349 (1997), 3737-3771.
MSC (1991): Primary 16A16, 16A24
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 16A16, 16A24

S. Caenepeel
Affiliation: Faculty of Applied Sciences, Free University of Brussels, VUB, Pleinlaan 2, B-1050 Brussels, Belgium
Email: scaenepe@vnet3.vub.ac.be

F. Van Oystaeyen
Affiliation: Department of Mathematics, University of Antwerp, UIA, Universiteitsplein 1, B-2610 Wilrijk, Belgium
Email: francin@wins.uia.ac.be

Y. H. Zhang
Affiliation: Department of Mathematics, University of Antwerp, UIA, Universiteitsplein 1, B-2610 Wilrijk, Belgium
Email: zhang@wins.uia.ac.be

DOI: 10.1090/S0002-9947-97-01839-4
PII: S 0002-9947(97)01839-4
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.
Copyright of article: Copyright 1997, American Mathematical Society

Fred Van Oystaeyen and Yinhuo Zhang, The Brauer group of a braided monoidal category, Journal of Algebra 202 (1998), 96-128.

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