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Funktsional. Anal. i Prilozhen., 2013, Volume 47, Issue 2, Pages 55–67 (Mi faa3112)  

This article is cited in 1 scientific paper (total in 1 paper)

KMS States on $\mathfrak{S}_\infty$ Invariant with Respect to the Young Subgroups

N. I. Nessonov

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar'kov

Abstract: Let $\mathfrak{S}_\mathbb{X}$ be the group of all finite permutations on a countable set $\mathbb {X}$, and let $\Pi=( ^1\mathbb{X},…, ^n\mathbb{X})$ be a partition of $\mathbb{X}$ into disjoint subsets such that $| ^i\mathbb{X}|=\infty$ for all $i$. We set $\mathfrak{S}_\Pi=\{s\in\mathfrak{S}_\mathbb{X}\mid s( ^i\mathbb{X})= ^i\mathbb{X}$ for all $i\}$. A positive definite function $\varphi$ on $\mathfrak{S}_\mathbb{X}$ is called a KMS state if the corresponding vector in the space of the GNS representation is cyclic for the commutant of this representation. A complete description of all factor KMS states which are invariant (central) with respect to the subgroup $\mathfrak{S}_\Pi$ is obtained.

Keywords: KMS state, indecomposable state, Young subgroup, factor representation, quasi-equivalent representations

DOI: https://doi.org/10.4213/faa3112

Full text: PDF file (241 kB)
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English version:
Functional Analysis and Its Applications, 2013, 47:2, 127–137

Bibliographic databases:

UDC: 517.986.4
Received: 12.01.2011

Citation: N. I. Nessonov, “KMS States on $\mathfrak{S}_\infty$ Invariant with Respect to the Young Subgroups”, Funktsional. Anal. i Prilozhen., 47:2 (2013), 55–67; Funct. Anal. Appl., 47:2 (2013), 127–137

Citation in format AMSBIB
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\paper KMS States on $\mathfrak{S}_\infty$ Invariant with Respect to the Young Subgroups
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\pages 55--67
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. A. Neretin, “Infinite symmetric groups and combinatorial constructions of topological field theory type”, Russian Math. Surveys, 70:4 (2015), 715–773  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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