arXiv math/03050442003-05math.OA

KMS states on C*-algebras associated to expansive maps

Alex Kumjian, Jean Renault

备注：: 9 pages, minor changes, submitted to Proceedings of the AMS

英文摘要：

Using Walters' version of the Ruelle-Perron-Frobenius Theorem we show the existence and uniqueness of KMS states for a certain one-parameter group of automorphisms on a C*-algebra associated to a positively expansive map on a compact metric space.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Exact circle maps and KMS states

We describe the KMS-states and the ground states for the gauge action on the C*-algebra of the oriented transformation groupoid of a continuous piecewise monotone and exact map of the circle.

2013-01-19math.OA

Radon--Nikodym representations of Cuntz--Krieger algebras and Lyapunov spectra for KMS states

We study relations between $(H,β)$--KMS states on Cuntz--Krieger algebras and the dual of the Perron--Frobenius operator $\mathcal{L}_{-βH}^{*}$. Generalising the well--studied purely hyperbolic situation, we obtain under mild conditions that for an expansive dynamical system there is a one--one correspondence between $(H,β)$--KMS states and eigenmeasures of $\mathcal{L}_{-βH}^{*}$ for the eigenvalue 1. We then consider representations of Cuntz--Krieger algebras which are induced by Markov fibred systems, and show that if the associated incidence matrix is irreducible then these are $\ast$--is…

2006-07-07math.DSmath.OA

KMS and ground states on ultragraph C*-algebras

We describe KMS and ground states arising from a generalized gauge action on ultragraph C*-algebras. We focus on ultragraphs that satisfy Condition~(RFUM), so that we can use the partial crossed product description of ultragraph C*-algebras recently described by the second author and Danilo Royer. In particular, for ultragraphs with no sinks, we generalize a recent result by Toke Carlsen and Nadia Larsen: Given a time evolution on the C*-algebra of an ultragraph, induced by a function on the edge set, we characterize the KMS states in five different ways and ground states in four different way…

2017-10-25math.DSmath.OA

KMS States, Entropy and the Variational Principle in full C*-dynamical systems

To any periodic, unital and full C*-dynamical system (A, α, R) an invertible operator s acting on the Banach space of trace functionals of the fixed point algebra is canonically associated. KMS states correspond to positive eigenvectors of s. A Perron-Frobenius type theorem asserts the existence of KMS states at inverse temperatures equal the logarithms of the inner and outer spectral radii of s (extremal KMS states). Examples arising from subshifts in symbolic dynamics, self-similar sets in fractal geometry and noncommutative metric spaces are discussed. Certain subshifts are naturally associ…

2000-03-15math.DSmath.OA

C*-algebras associated with interval maps

For each piecewise monotonic map tau of [0,1], we associate a pair of C*-algebras F_tau and O_tau and calculate their K-groups. The algebra F_tau is an AI-algebra. We characterize when F_tau and O_τare simple. In those cases, F_tau has a unique trace, and O_tau is purely infinite with a unique KMS-state. In the case that tau is Markov, these algebras include the Cuntz-Krieger algebras O_A, and the associated AF-algebras F_A. Other examples for which the K-groups are computed include tent maps, quadratic maps, multimodal maps, interval exchange maps, and beta-transformations. For the case of in…

2005-10-14math.DSmath.OA

$C^*$-algebras associated with algebraic correspondences on the Riemann sphere

Let $p(z,w)$ be a polynomial in two variables. We call the solution of the algebraic equation $p(z,w) = 0$ the algebraic correspondence. We regard it as the graph of the multivalued function $z \mapsto w$ defined implicitly by $p(z,w) = 0$. Algebraic correspondences on the Riemann sphere $\hat{\mathbb C}$ give a generalization of dynamical systems of Klein groups and rational functions. We introduce $C^*$-algebras associated with algebraic correspondences on the Riemann sphere. We show that if an algebraic correspondence is free and expansive on a closed $p$-invariant subset $J$ of $\hat{\math…

2008-06-22math.DSmath.OA

更多相关论文收起更多论文

关于与可数对一映射的转移算子相关的 $C^*$-代数

On $C^*$-algebras associated to transfer operators for countable-to-one maps

本文为可数对一映射的转移算子构造泛交叉积 $C_0(X)\rtimes L$，给出加权复合算子表示，并研究其与已知 $C^*$-代数的关系、单性、唯一性、Kirchberg 判据及 KMS 态。

2023-07-12math.DSmath.OA