Abstract
Let H be a Hopf algebra with bijective antipode, α, β ∈ Aut Hopf (H) and M a finite dimensional (α, β)-Yetter-Drinfeld module. We prove that End(M) endowed with certain structures becomes an H-Azumaya algebra, and the set of H-Azumaya algebras of this type is a subgroup of BQ(k, H), the Brauer group of H.
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References
Caenepeel, S., Van Oystaeyen, F., Zhang, Y.: Quantum Yang-Baxter module algebras. K-Theory 8, 231–255 (1994)
Caenepeel, S., Van Oystaeyen, F., Zhang, Y.: The Brauer group of Yetter-Drinfeld module algebras. Trans. Am. Math. Soc. 349, 3737–3771 (1997)
Connes, A., Moscovici, H.: Hopf algebras, cyclic cohomology and the transverse index theorem. Commun. Math. Phys. 198, 199–264 (1998)
Connes, A., Moscovici, H.: Cyclic cohomology and Hopf algebra symmetry. Lett. Math. Phys. 52, 1–28 (2000)
Hajac, P.M., Khalkhali, M., Rangipour, B., Sommerhäuser, Y.: Stable anti-Yetter-Drinfeld modules. C. R. Math. Acad. Sci. Paris 338, 587–590 (2004)
Hajac, P.M., Khalkhali, M., Rangipour, B., Sommerhäuser, Y.: Hopf-cyclic homology and cohomology with coefficients. C. R. Math. Acad. Sci. Paris 338, 667–672 (2004)
Jara, P., Ştefan, D.: Hopf-cyclic homology and relative cyclic homology of Hopf-Galois extensions. Proc. Lond. Math. Soc. 93, 138–174 (2006)
Kassel, C.: Quantum groups. In: Graduate Texts in Mathematics, vol. 155. Springer, Berlin (1995)
Majid, S.: Foundations of Quantum Group Theory. Cambridge University Press, Cambridge (1995)
Panaite, F., Staic, M.D.: Generalized (anti) Yetter-Drinfeld modules as components of a braided T-category. Isr. J. Math. 158, 349–365 (2007)
Sweedler, M.E.: Hopf Algebras. Benjamin, New York (1969)
Turaev, V.: Homotopy field theory in dimension 3 and crossed group-categories. arXiv:math.GT/0005291 (2000)
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Research carried out while the first author was visiting the University of Antwerp, supported by a postdoctoral fellowship offered by FWO (Flemish Scientific Research Foundation). This author was also partially supported by the programme CEEX of the Romanian Ministry of Education and Research, contract nr. 2-CEx06-11-20/2006.
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Panaite, F., Van Oystaeyen, F. Quasi-elementary H-Azumaya Algebras Arising from Generalized (Anti) Yetter-Drinfeld Modules. Appl Categor Struct 19, 803–820 (2011). https://doi.org/10.1007/s10485-009-9213-4
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DOI: https://doi.org/10.1007/s10485-009-9213-4