Open quantum subgroups of locally compact quantum groups
Open quantum subgroups of locally compact quantum groups
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局部紧量子群的开量子子群
DOI：
10.1016/j.aim.2012.09.002
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
P. Sołtan
中科院分区：
文献类型：
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作者：
Matthew Daws;P. Kasprzak;Adam G. Skalski;P. Sołtan
研究了局部紧量子群的闭量子子群的基本概念。两个定义-一个由于S. Vaes和一个由于S.L. Woronowicz -分析和它们之间的关系进行了讨论。在许多重新表述，我们证明了前一个定义可以措辞的量子群的表示的准等价，而后者可以与一个旧的定义Podlewald从紧量子群的理论。在经典群、经典群的群、紧量子群和离散量子群的情形下，证明了这两个定义的等价性。本文还建立了与经典调和分析的Herz限制定理的量子群推广的深刻关系，特别地，在我们的分析过程中，我们给出了Herz限制定理的一个新的证明。
We investigate the fundamental concept of a closed quantum subgroup of a locally compact quantum group. Two definitions — one due to S. Vaes and one due to S.L. Woronowicz — are analyzed and relations between them discussed. Among many reformulations we prove that the former definition can be phrased in terms of quasi-equivalence of representations of quantum groups while the latter can be related to an old definition of Podleś from the theory of compact quantum groups. The cases of classical groups, duals of classical groups, compact and discrete quantum groups are singled out and equivalence of the two definitions is proved in the relevant context. A deep relationship with the quantum group generalization of the Herz restriction theorem from classical harmonic analysis is also established, in particular, in the course of our analysis we give a new proof of the Herz restriction theorem.