The Brauer group of Yetter-Drinfel’d module algebras

Caenepeel, S.; Oystaeyen, F.; Zhang, Y.

doi:10.1090/S0002-9947-97-01839-4

The Brauer group of Yetter-Drinfel’d module algebras
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by S. Caenepeel, F. Van Oystaeyen and Y. H. Zhang PDF

Trans. Amer. Math. Soc. 349 (1997), 3737-3771 Request permission

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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