离散量子群的 SAT 作用及其冯诺伊曼代数的最小注入扩展

IF 0.8 3区数学 Q2 MATHEMATICS Proceedings of the American Mathematical Society Pub Date : 2024-04-24 DOI:10.1090/proc/16882

Mehrdad Kalantar, Fatemeh Khosravi, Mohammad Moakhar

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引用次数: 0

摘要

我们为局部紧凑量子群的作用引入了强近似传递（SAT）态概念的自然概括。在 Kac 型离散量子群的情况下，我们证明了唯一静止 SAT 状态的存在会带来关于量子群冯-诺伊曼代数注入扩展的刚性结果。

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SAT actions of discrete quantum groups and minimal injective extensions of their von Neumann algebras

We introduce a natural generalization of the notion of strongly approximately transitive (SAT) states for actions of locally compact quantum groups. In the case of discrete quantum groups of Kac type, we show that the existence of unique stationary SAT states entails rigidity results concerning injective extensions of quantum group von Neumann algebras.

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.