Abstract
For a field k and two finite groups G and X, when G acts on X from the right by group automorphisms, there is a Hopf algebra structure on k-space (kX op)* ⋇ kG (see Theorem 2.1), called a non-balanced quantum double and denoted by D X (G). In this paper, some Hopf algebra properties of D X (G) are given, the representation types of D X (G) viewed as a k-algebra are discussed, the algebra structure and module category over D X (G) are studied. Since the Hopf algebra structure of non-balanced quantum double D X (G) generalizes the usual quantum double D(G) for a finite group G, all results about D X (G) in this paper can also be used to describe D(G) as a special case and the universal R-matrix of D X (G) provides more solutions of Yang-Baxter equation.
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Supported by Doctoral Foundation of Qingdao University of Science and Technology (20080022398), the National Natural Science Foundation of China (11271318, 11171296), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (20110101110010).
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Chen, Ll., Li, F. On the structure and representations of non-balanced quantum doubles. Appl. Math. J. Chin. Univ. 27, 475–488 (2012). https://doi.org/10.1007/s11766-012-2852-5
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DOI: https://doi.org/10.1007/s11766-012-2852-5