Compact quantum group structures on type-I $\mathrm{C}^*$-algebras

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Noncommutative Geometry Pub Date : 2020-08-09 DOI:10.4171/jncg/516

A. Chirvasitu, Jacek Krajczok, P. Sołtan

引用次数: 0

Abstract

We prove a number of results having to do with equipping type-I $\mathrm{C}^*$-algebras with compact quantum group structures, the two main ones being that such a compact quantum group is necessarily co-amenable, and that if the $\mathrm{C}^*$-algebra in question is an extension of a non-zero finite direct sum of elementary $\mathrm{C}^*$-algebras by a commutative unital $\mathrm{C}^*$-algebra then it must be finite-dimensional.

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i - $\ mathm {C}^*$-代数上的紧量子群结构

我们证明了一些关于给i型$\ mathm {C}^*$-代数配紧量子群结构的结果，其中两个主要的证明是:这种紧量子群必然是可协的;如果所讨论的$\ mathm {C}^*$-代数是$\ mathm {C}^*$-代数的非零有限直和由可交换一元$\ mathm {C}^*$-代数扩展，那么它一定是有限维的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Noncommutative Geometry 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Noncommutative Geometry covers the noncommutative world in all its aspects. It is devoted to publication of research articles which represent major advances in the area of noncommutative geometry and its applications to other fields of mathematics and theoretical physics. Topics covered include in particular: Hochschild and cyclic cohomology K-theory and index theory Measure theory and topology of noncommutative spaces, operator algebras Spectral geometry of noncommutative spaces Noncommutative algebraic geometry Hopf algebras and quantum groups Foliations, groupoids, stacks, gerbes Deformations and quantization Noncommutative spaces in number theory and arithmetic geometry Noncommutative geometry in physics: QFT, renormalization, gauge theory, string theory, gravity, mirror symmetry, solid state physics, statistical mechanics.