The temperature state space of a \(C^ *\)-dynamical system. II
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.
scientific article; zbMATH DE number 3971532