De finetti-type theorems on quasi-local algebras and infinite fermi tensor products

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-01-07 DOI:10.1142/s021902572250028x

V. Crismale, S. Rossi, Paola Zurlo

引用次数: 4

Abstract

Local actions of PN, the group of finite permutations on N, on quasi-local algebras are defined and proved to be PNabelian. It turns out that invariant states under local actions are automatically even, and extreme invariant states are strongly clustering. Tail algebras of invariant states are shown to obey a form of the Hewitt and Savage theorem, in that they coincide with the fixed-point von Neumann algebra. Infinite graded tensor products of C∗-algebras, which include the CAR algebra, are then addressed as particular examples of quasi-local algebras acted upon PN in a natural way. Extreme invariant states are characterized as infinite products of a single even state, and a de Finetti theorem is established. Finally, infinite products of factorial even states are shown to be factorial by applying a twisted version of the tensor product commutation theorem, which is also derived here. Mathematics Subject Classification: 46L06, 60G09, 60F20, 46L53.

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准局部代数和无限费米张量积上的定精细型定理

定义了拟局部代数上N上有限置换群PN的局部作用，并证明了它们是PNabelian的。结果表明，局部作用下的不变量状态是自动偶的，极端不变量状态是强聚类的。不变状态的尾代数服从Hewitt和Savage定理的一种形式，因为它们与不动点冯·诺伊曼代数一致。C * -代数的无限次阶张量积，其中包括CAR代数，然后作为以自然方式作用于PN的拟局部代数的特殊例子来处理。将极端不变状态描述为单个偶态的无穷积，并建立了一个de Finetti定理。最后，通过应用张量积交换定理的一个扭曲版本，证明了阶乘偶态的无穷积是阶乘的，这个定理也是在这里推导出来的。数学学科分类:46L06、60G09、60F20、46L53。

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

Infinite Dimensional Analysis Quantum Probability and Related Topics 数学-统计学与概率论

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： In the past few years the fields of infinite dimensional analysis and quantum probability have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. The number of first-class papers in these fields has grown at the same rate. This is currently the only journal which is devoted to these fields. It constitutes an essential and central point of reference for the large number of mathematicians, mathematical physicists and other scientists who have been drawn into these areas. Both fields have strong interdisciplinary nature, with deep connection to, for example, classical probability, stochastic analysis, mathematical physics, operator algebras, irreversibility, ergodic theory and dynamical systems, quantum groups, classical and quantum stochastic geometry, quantum chaos, Dirichlet forms, harmonic analysis, quantum measurement, quantum computer, etc. The journal reflects this interdisciplinarity and welcomes high quality papers in all such related fields, particularly those which reveal connections with the main fields of this journal.