由可数离散群的扭曲作用诱导的$C^*$-代数包含的强Morita等价

IF 0.3 4区数学 Q4 MATHEMATICS

Mathematica Scandinavica Pub Date : 2019-10-09 DOI:10.7146/math.scand.a-125997

K. Kodaka

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引用次数: 5

摘要

我们考虑$\sigma$-酉$C^*$-代数上可数离散群的两个扭曲作用。然后通过取约化叉积，得到了$C^*$-代数的两个包含。我们假设它们作为$C^*$-代数的包含是强Morita等价的。此外，我们假设$C^*$-代数的一个包含是不可约的，也就是说，$\∑$-单位$C^**$-代数中的一个在约化扭叉积的乘法器$C^*.代数中的相对交换是平凡的。我们证明了这两个作用在群的某些自同构上是强森田等价的。

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Strong Morita equivalence for inclusions of $C^*$-algebras induced by twisted actions of a countable discrete group

We consider two twisted actions of a countable discrete group on $\sigma$-unital $C^*$-algebras. Then by taking the reduced crossed products, we get two inclusions of $C^*$-algebras. We suppose that they are strongly Morita equivalent as inclusions of $C^*$-algebras. Also, we suppose that one of the inclusions of $C^*$-algebras is irreducible, that is, the relative commutant of one of the $\sigma$-unital $C^*$-algebra in the multiplier $C^*$-algebra of the reduced twisted crossed product is trivial. We show that the two actions are then strongly Morita equivalent up to some automorphism of the group.

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来源期刊

Mathematica Scandinavica 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematica Scandinavica is a peer-reviewed journal in mathematics that has been published regularly since 1953. Mathematica Scandinavica is run on a non-profit basis by the five mathematical societies in Scandinavia. It is the aim of the journal to publish high quality mathematical articles of moderate length. Mathematica Scandinavica publishes about 640 pages per year. For 2020, these will be published as one volume consisting of 3 issues (of 160, 240 and 240 pages, respectively), enabling a slight increase in article pages compared to previous years. The journal aims to publish the first issue by the end of March. Subsequent issues will follow at intervals of approximately 4 months. All back volumes are available in paper and online from 1953. There is free access to online articles more than five years old.