部分紧量子群
Partial compact quantum groups
摘要：
紧的面型量子群，由Hayashi引入，形成一类紧的量子群胚，具有经典的有限集的对象。利用弱乘子双代数和弱乘子霍普夫代数的概念（分别是由于B{<$}hm--Gómez-Torrecillas--López-Centella和Van Daele-Wang），我们推广了Hayashi的定义以允许无限对象集，并将所得对象称为部分紧量子群。利用部分融合C $^*$ -范畴的概念，证明了这类部分紧量子群的Tannaka-Kre $\breve{\textrmı}$ n-Woronowicz重构结果.作为例子，我们从部分紧量子群的观点考虑了动力学量子$SU(2)$ -群。
英文摘要：
Compact quantum groups of face type, as introduced by Hayashi, form a class of compact quantum groupoids with a classical, finite set of objects. Using the notions of a weak multiplier bialgebra and weak multiplier Hopf algebra (resp. due to B{ö}hm--Gómez-Torrecillas--López-Centella and Van Daele-Wang), we generalize Hayashi's definition to allow for an infinite set of objects, and call the resulting objects partial compact quantum groups. We prove a Tannaka-Kre$\breve{\textrmı}$n-Woronowicz reconstruction result for such partial compact quantum groups using the notion of a partial fusion C$^*$-category. As examples, we consider the dynamical quantum $SU(2)$-groups from the point of view of partial compact quantum groups.
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