量子对称群的投射极限与霍普夫代数的二重构造
Projective limits of quantum symmetry groups and the doubling construction for Hopf algebras
摘要：
证明了具有正交滤子的C*-代数的归纳极限的量子对称群是序列中出现的C* 代数的量子对称群的投射极限.一些明确的例子，这样的投射极限进行了研究，包括有限对称群，不适合直接进入框架的主要定理，需要进一步的具体研究的量子对称群的情况。这些研究揭示了离散群的量子对称群与霍普夫代数的二重构造之间的深刻联系。
英文摘要：
The quantum symmetry group of the inductive limit of C*-algebras equipped with orthogonal filtrations is shown to be the projective limit of the quantum symmetry groups of the C*-algebras appearing in the sequence. Some explicit examples of such projective limits are studied, including the case of quantum symmetry groups of the duals of finite symmetric groups, which do not fit directly into the framework of the main theorem and require further specific study. The investigations reveal a deep connection between quantum symmetry groups of discrete group duals and the doubling construction for Hopf algebras.
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