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The quantum disk is not a quantum group
Journal of Topology and Analysis ( IF 0.5 ) Pub Date : 2021-07-22 , DOI: 10.1142/s1793525321500436
Jacek Krajczok 1 , Piotr M. Sołtan 2
Affiliation  

In this paper, we show that the quantum disk, i.e. the quantum space corresponding to the Toeplitz C*-algebra does not admit any compact quantum group structure. We prove that if such a structure existed the resulting compact quantum group would simultaneously be of Kac type and not of Kac type. The main tools used in the solution come from the theory of operators on Hilbert spaces.



中文翻译:

量子盘不是一个量子群

在本文中,我们展示了量子盘,即托普利茨对应的量子空间C*-代数不承认任何紧凑的量子群结构。我们证明,如果存在这样的结构,那么由此产生的紧量子群将同时属于 Kac 型而不是 Kac 型。解决方案中使用的主要工具来自希尔伯特空间上的算子理论。

更新日期:2021-07-22
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