Abstract
It is known that any strict tensor category (C,⊗,I) can determine a strict braided tensor categoryZ(C), the centre ofC. WhenA is a finite Hopf algebra, Drinfel’d has proved thatZ( AM) is equivalent toD(A)M as a braided tensor category, whereAM is the left A-module category, andD(A) is the Drinfel’d double ofA. This is the categorical interpretation ofD(A). Z( AM) is proved to be equivalent to the Yetter-Drinfel’d module category,AYD A as a braided tensor category for any Hopf algebraA. Furthermore, for right A-comodule categoryM A, Z(MA) is proved to be equivalent to the Yetter-Drinfel’d module categoryAY DA as a braided tensor category. But,in the two cases, the Yetter-Drinfel’d module categoryAY DA has different braided tensor structures.
Similar content being viewed by others
References
David, E. R., Jacoh, T., Yetter-Drinfel’d categories asswiated to an arbitrary lrialgehra,J. Algebra, 1993, 187: 259.
Lamhe, L. A., Radford, D. E., Algebraic aspects of the quantum Yang-Baxter equation,J. Algebra, 1993, 154: 228.
Kassel, C., Turaev, V., Double construction for monoidal catrgories,Acta Math., 1995, 175: 1.
Kassrl, C., Quantum groups,Graduate Texts in Math., New York: Springer-Verlag. 1995, 155.
Drinfel’d, V. G., Quantum groups, inProreedings of the ICM, Rhode Island: AMS, 1987, pp. 798–820.
Yetter, D. N., Quantum groups and representations of monoidal categorics,Math. Proc. Cambridge Philos. Soc., 1990, 108: 261.
Author information
Authors and Affiliations
About this article
Cite this article
Kan, H., Wang, S. A categorical interpretation of Yetter-Drinfel’d modules. Chin. Sci. Bull. 44, 771–778 (1999). https://doi.org/10.1007/BF02885017
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02885017