Abstract
We study the tensor category of modules over a semisimple bialgebra H under the assumption that irreducible H-modules of the same dimension > 1 are isomorphic. We consider properties of Clebsch–Gordan coefficients showing multiplicities of occurrences of each irreducible H-module in a tensor product of irreducible ones. It is shown that, in general, these coefficients cannot have small values.
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Acknowledgments
The authors are grateful to the referee for valuable remarks and suggestions. Research partially supported by grants DFG, RFBR 09-01-00058, 09-01-90416-Ucr-f-a.
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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Artamonov, V.A., Mukhatov, R.B. & Wisbauer, R. On the category of modules over some semisimple bialgebras. Arab. J. Math. 1, 29–38 (2012). https://doi.org/10.1007/s40065-012-0010-9
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DOI: https://doi.org/10.1007/s40065-012-0010-9