On the Conjugacy of Measurable Partitions with Respect to the Normalizer of a Full Type \(\mathrm{II}_1\) Ergodic Group

IF 0.6 4区 数学 Q3 MATHEMATICS
Andrei Lodkin, Benzion Rubshtein
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引用次数: 0

Abstract

Let \(G\) be a countable ergodic group of automorphisms of a measure space \((X,\mu)\) and \(\mathcal{N}[G]\) be the normalizer of its full group \([G]\). Problem: for a pair of measurable partitions \(\xi\) and \(\eta\) of the space \(X\), when does there exist an element \(g\in\mathcal{N}[G]\) such that \(g\xi=\eta\)? For a wide class of measurable partitions, we give a solution to this problem in the case where \(G\) is an approximately finite group with finite invariant measure. As a consequence, we obtain results concerning the conjugacy of the commutative subalgebras that correspond to \(\xi\) and \(\eta\) in the type \(\mathrm{II}_1\) factor constructed via the orbit partition of the group \(G\).

论相对于全类型 $$mathrm{II}_1$ 尔后组归一化的可测分区的共轭性
Abstract Let \(G\) be a countable ergodic group of automorphisms of a measure space \((X,\mu)\) and \(\mathcal{N}[G]\) be the normalizer of its full group \([G]\).问题:对于空间 \(X\) 的一对可测分区 \(\xi\) 和 \(\eta\) ,什么时候存在一个元素 \(g\in\mathcal{N}[G]\) 使得 \(g\xi=\eta\) ?对于一类广泛的可测分区,我们给出了在\(G\) 是具有有限不变度量的近似有限群的情况下这个问题的解决方案。因此,我们得到了通过群 \(G\) 的轨道分区构造的 \(\mathrm{II}_1\) 因子类型中对应于 \(\xi\) 和 \(\eta\) 的交换子代数的共轭结果。
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
7
审稿时长
>12 weeks
期刊介绍: Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.
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