Categorically Morita Equivalent Compact Quantum Groups
Categorically Morita Equivalent Compact Quantum Groups
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DOI：
10.25537/dm.2018v23.2165-2216
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发表时间：
2017-04
影响因子：
0.9
通讯作者：
S. Neshveyev;M. Yamashita
中科院分区：
文献类型：
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作者：
S. Neshveyev;M. Yamashita
给出了紧量子群之间范畴Morita等价的动力学刻画。更确切地说，通过Tannaka-Krein型对偶，赋予两个紧致量子群的交换作用的单位C*-代数对应于它们的表示范畴上的双模范畴。我们表明，这个双模范畴是可逆的当且仅当行动是免费的，有限维不动点代数，这是在对偶Frobenius代数在适当的意义。这扩展了著名的monoidal等价的双霍普夫伽罗瓦对象的特征。
We give a dynamical characterization of categorical Morita equivalence between compact quantum groups. More precisely, by a Tannaka-Krein type duality, a unital C*-algebra endowed with commuting actions of two compact quantum groups corresponds to a bimodule category over their representation categories. We show that this bimodule category is invertible if and only if the actions are free, with finite dimensional fixed point algebras, which are in duality as Frobenius algebras in an appropriate sense. This extends the well-known characterization of monoidal equivalence in terms of bi-Hopf-Galois objects.