非奇异Bernoulli叉积的分类结果

IF 0.7 3区数学 Q2 MATHEMATICS

Studia Mathematica Pub Date : 2022-02-15 DOI:10.4064/sm220217-11-5

S. Vaes, Bram Verjans

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引用次数: 0

摘要

我们证明了自由群和更一般的自由积群的非奇异伯努利作用给出的III型因子的刚性和分类结果。这包括一大类类型为III$_1$的非同构伯努利交叉乘积，这些乘积不能用Connes$\tau$不变量来区分。这是在经过充分研究的概率测度保持情况之外的第一个这样的分类结果。

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Classification results for nonsingular Bernoulli crossed products

We prove rigidity and classification results for type III factors given by nonsingular Bernoulli actions of the free groups and more general free product groups. This includes a large family of nonisomorphic Bernoulli crossed products of type III$_1$ that cannot be distinguished by Connes $\tau$-invariant. These are the first such classification results beyond the well studied probability measure preserving case.

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来源期刊

Studia Mathematica 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

5 months

期刊介绍： The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.