The temperature state space of a \(C^ *\)-dynamical system. II
type: Item
instance of: scholarly article
title: The temperature state space of a \(C^ *\)-dynamical system. II
zbMATH Open document ID: 0602.46067
DOI: 10.2307/1971271
author: Ola Bratteli
author: George A. Elliott
author: Akitaka Kishimoto
published in: Annals of Mathematics. Second Series
publication date: 1986-01-01T00:00:00Z
review text: The space of KMS-states at finite inverse temperatures of a dynamical system (A,\(\gamma)\), where A is a simple unital \(C^*\)-algebra and \(\gamma\) is a faithful representation of a Lie group \(\Gamma\) as automorphisms of A, is a locally compact bundle of simplices over the space of finite inverse temperatures, which may be identified with the Lie algebra of \(\Gamma\), such that the space of continuous real-valued functions on this bundle which are affine on fibres separates points. In the case that the Lie algebra of \(\Gamma\) is \({\mathbb{R}}\), the authors showed in the Part I of this paper [Yokohama Math. J. 28, 125-167 (1980; Zbl 0466.46057)] that any metrizable such bundle of simplices, in this case over \({\mathbb{R}}\), arises in this way. In this Part II the mentioned result is extended to the case of \({\mathbb{R}}^ n\). This demonstrates the occurence of arbitrary phase diagrams with finitely many parameters, which could be thought of as thermodynamical variables such as temperature and chemical potential.
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L30
Mathematics Subject Classification ID: 82B10
Mathematics Subject Classification ID: 46L40
Mathematics Subject Classification ID: 46L60
zbMATH DE Number: 3971532
zbMATH Keywords: KMS-states
zbMATH Keywords: finite inverse temperatures
zbMATH Keywords: dynamical system
zbMATH Keywords: faithful representation of a Lie group
zbMATH Keywords: Lie algebra
zbMATH Keywords: bundle of simplices
zbMATH Keywords: phase diagrams
reviewed by: Sh. A. Ayupov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/1971271
OpenAlex ID: W2320470282
description: scientific article; zbMATH DE number 3971532