Klaus Thomsen
KMS weights for generalized gauge actions on graph C*-algebras are studied and a complete description of the structure is obtained for the gauge action when the graph is strongly connected and has at most countably many exits. The structure is surprisingly rich.
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
KMS states on finite-graph C*-algebras
研究了具有汇和源的有限图C* 代数上的KMS态。我们比较了有限图C* 代数-代数和与有理函数的复动力系统相关的C* 代数-代数。我们表明，如果逆温度$β$是大的，那么一组极端的$β$ -KMS的状态是参数化的一组水槽的图。这意味着图的汇对应于从KMS状态点开始的有理函数的分支点。因为我们考虑了有汇和源的图，所以相关双模的左作用不是内射的。然后将伴随图C* 代数实现为Katalina所研究的（相对）Cuntz-Pimsner代数.我们需要将Cuntz-Pimsner代数上构造KMS态的Laca-Neshevyev定理推广到双模的左作用不是内射的情况。
We study KMS states for gauge actions with potential functions on Cuntz--Krieger algebras whose underlying one-sided topological Markov shifts are continuous orbit equivalent. As a result, we have a certain relationship between topological entropy of continuous orbit equivalent one-sided topological Markov shifts.
Hausdorff Measures and KMS States
给定一个紧度量空间$X$和一个满足局部标度性质的局部同胚$T:X\to X$，我们证明了$X$上的Hausdorff测度在自然地与对$(X,T)$相关联的$C^{*}$ -代数上产生一个KMS态，使得逆温度与豪斯多夫维数一致.我们证明了KMS态在一些温和的假设下是唯一的。我们用我们的结果来描述KMS状态的Cuntz代数，图代数，和$C^{*}$ -代数上的分形。
KMS states on C^*-algebras associated with self-similar sets
本文研究了C ${}^*$ -代数上的规范作用量的KMS态，其中C-代数的自相似集的分支点是有限的。如果自相似集不包含任何分支点，则Hutchinson测度给出唯一的KMS状态。但当自相似集含有一个分支点时，有时会出现来自分支点的其它KMS态。为此，我们明确地构造了一个基的Hilbert C ${}^*$ -模与自相似集有限分支条件。利用这一点，我们得到了K上的Borel概率测度扩张到与原自相似集相关联的C ${}^*$ -代数上的KMS态的条件.我们对单位区间动力学和与复动力系统相关的Sierpinski垫片的KMS态进行了分类。如果$β$等于$\log N$，则这些示例的KMS状态是唯一的，并且由哈钦森测度给出，其中$N$是收缩的数量。如果$β> \log N$满足，则它们被表示为由分支点轨道上支持的度量给出的KMS状态的凸组合。
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…
Given a self-similar $K$ set defined from an iterated function system $Γ=(γ_1,\ldots,γ_n)$ and a set of function $H=\{h_i:K\to\mathbb{R}\}_{i=1}^d$ satisfying suitable conditions, we define a generalized gauge action on Kawjiwara-Watatani algebras $\mathcal{O}_Γ$ and their Toeplitz extensions $\mathcal{T}_Γ$. We then characterize the KMS states for this action. For each $β\in(0,\infty)$, there is a Ruelle operator $\mathcal{L}_{H,β}$ and the existence of KMS states at inverse temperature $β$ is related to this operator. The critical inverse temperature $β_c$ is such that $\mathcal{L}_{H,β_c}$ …
We generalise a number of classical results from the theory of KMS states to KMS weights in the setting of $C^{*}$-dynamical systems arising from a continuous groupoid homomorphism $c:\mathcal{G} \to \mathbb{R}$ on a locally compact second countable Hausdorff étale groupoid $\mathcal{G}$. In particular, we generalise Neshveyev's Theorem to KMS weights.
Radon--Nikodym representations of Cuntz--Krieger algebras and Lyapunov spectra for KMS states
研究了Cuntz-Krieger代数上的$(H,β)$ -KMS态与Perron-Frobenius算子$\mathcal{L}_{-βH}^{*}$的对偶之间的关系.推广研究纯双曲的情况下，我们得到在温和的条件下，对于一个膨胀的动力系统有一个一-一个对应的$(H,β)$ -KMS状态和本征值1的$\mathcal{L}_{-βH}^{*}$的本征测度。然后，我们考虑表示的Cuntz-Krieger代数诱导的马尔可夫系统，并表明，如果相关的关联矩阵是不可约的，那么这些是$\ast$ -同构于给定的Cuntz-Krieger代数。最后，我们应用这些一般结果研究了可能含有抛物元的本质自由Kleinian群$G$极限集的重分形分解。我们证明，对于由$G$产生的Cuntz-Krieger代数，存在由与$G$有关的Bowen-系列映射的类似物的李雅普诺夫谱诱导的KMS态的解析族.此外，我们还得到了这些KMS态对$G$极限集上连续函数集的限制的豪斯多夫维数公式。如果$G$没有抛物元，则这个公式可以解释为与$G$相关的最大熵测度的奇异谱.
KMS states and branched points
我们完全分类的规范作用的KMS状态的$C^*$ -代数与一个有理函数$R$在我们以前的工作。规范作用量在$β= \log °R$有一个相变。从KMS态的结构可以得到$R$的度、分支点数、例外点数和例外点的轨道。我们也用类似的方法对与一些自相似集相关的$C^*$ -代数的KMS态进行了分类，这些自相似集包括满帐篷映射和Sierpinski垫片。
KMS weights on groupoid and graph C*-algebras
本文描述了第二可数局部紧Hausdorff标样广群的约化C* 代数上的单参数作用的KMS权，该广群产生于满足两个条件的连续实值同态.随后的结果被应用到确定的KMS权重的规范作用在一个单图代数。由极值KMS权重的GNSS表示生成的冯诺依曼代数是一个因子，并且开发了工具来确定其类型。最后，本文用三个例子来说明结果。
KMS States, Entropy and a Variational Principle for Pressure
我们想把熵和压力的概念与$C^*$ -代数的KMS态的概念联系起来。在我们的时代，熵有几种不同的定义。我们在这里描述的一个是相当自然的，并扩展了热力学形式主义理论中动力系统的通常一个。它的优点是很容易被引入。它基本上是从转移算子（也称为Ruelle算子）获得的。稍后我们引入压力的概念作为最小-最大原理。最后，我们考虑的概念KMS状态作为一个潜在的平衡态（在$C^*$ -代数的背景下），我们表明，有KMS状态之间的关系，某些代数来自连续变换和平衡测度。
The paper contains a description of a connection between diagonal actions and certain KMS weights on groupoid $C^{*}$-algebras. It furthermore contains the realization of a graph $C^{*}$-algebra of a countable graph as the groupoid $C^{*}$-algebra of a local homeomorphism and applies the theory obtained on these algebras.
In order to realize all possible KMS-bundles on the Jiang-Su algebra, we introduce a class of C*-algebras which we call rationally approximately finite dimensional (RAF). Using these, we show that for a given proper simplex bundle $(S, π)$ with a singleton $π^{-1}(\{0\})$ and a unital separable monotracial C*-algebra $A$ absorbing the Jiang-Su algebra tensorially (for instance, the irrational rotation algebra), there exists a flow on $A$ whose KMS-bundle is isomorphic to $(S, π)$.
We calculate the S-invariant of Connes for the von Neumann algebra factors arising from KMS-weights of a generalized gauge action on a simple graph C*-algebra when the associated measure on the infinite path space of the graph is dissipative under the action of the shift.
We determine the factor generated by the GNS-representation defined by a KMS-weight for a generalized gauge action on a simple graph C*-algebra when the corresponding measure on the path space of the graph is conservative for the shift. This is an improvment of Theorem 3.2 in arXives 1412.6762.
KMS-weights on C*-algebras
在本文中，我们建立了一个坚实的框架，KMS-重量的C*-代数。我们使用另一种定义比一个介绍了Combes，但证明他们是等价的。
KMS states on C*-algebras associated to expansive maps
利用Walters的Ruelle-Perron-Frobenius定理证明了紧度量空间上正可扩映射所对应的C* 代数上的某个单参数自同构群的KMS态的存在唯一性.
On the C*-algebra of a locally injective surjection and its KMS states
证明了紧致度量空间上的局部内射满射存在一个标准局部同胚扩张，使得相应的C* 代数同构.然后，这是在KMS状态的广义规范作用的可能的逆温度的研究中使用。
KMS states on C*-algebras associated to local homeomorphisms
对于C* 代数上的每一个希尔伯特双模，都存在圆在相应的Toeplitz代数和Cuntz-Pimsner代数上的自然规范作用量，因此自然动力学可以通过将这些规范作用量提升为实直线的作用量来获得。我们研究了紧空间上与局部同胚相关的双模族动力学的KMS态。对于大于某个临界值的反温度，我们在Toeplitz代数上找到了一个大的KMS态单形，并且我们证明了Cuntz-Pimsner代数上的所有KMS态的反温度至多为这个临界值.我们说明我们的结果，考虑有限图的单侧道路空间上的向后移位，在那里我们可以使用最近的结果KMS状态图代数，看看会发生什么事低于临界值。我们的结果KMS态的Cuntz-Pimsner代数的位移表明，最近的限制范围内的反温度得到的Replsen是尖锐的。
KMS states on the C*-algebra of a higher-rank graph and periodicity in the path space
研究了强连通有限k-图的C* 代数的KMS态.我们发现规范作用量只有一个单参数子组可以接纳KMS态。这个优选的动态的极端KMS状态的参数化的阿贝尔群，捕获的周期性在无限的道路空间的图形的字符。我们得到了存在唯一KMS态的充要条件是k-图C* 代数是单的，从而完整地回答了Yang的一个问题.当k-图C* 代数-代数不简单时，我们的结果揭示了其Toeplitz扩张的一个意想不到的性质的相变.
KMS states on the C*-algebras of finite graphs
本文考虑有限有向图E，把它的Toeplitz-Cuntz-Krieger代数上的规范作用看作是R的作用。对于大于临界值β_c的反温度，我们给出了所有KMS_β态的显式构造。如果图是强连通的，则存在唯一的KMS_{β_c}状态，并且该状态通过商映射因子化到图的C* 代数C*（E）上。我们的方法是直接的和相对初级的。
We examine the theory of the KMS states on Pimsner algebras arising from multivariable unital C*-dynamical systems. As an application we show that Pimsner algebras of piecewise conjugate classical systems attain the same KMS states, even though it is still an open problem whether or not they are $*$-isomorphic.
The structure of KMS states of Toeplitz algebras associated to finite graphs equipped with the gauge action is determined by an Huef--Laca--Raeburn--Sims. Their results imply that extremal KMS states of type I correspond to vertices, while extremal KMS states at critical inverse temperatures correspond to minimal strongly connected components. The purpose of this article is to clarify the role of non-minimal components and the relation between vertices and minimal components in the KMS-structure. For each component $C_0$ and each vertex $v \in C_0$, the KMS states at the critical inverse tempe…
KMS States, Entropy and the Variational Principle in full C*-dynamical systems
对于任何周期的、单位的、满的C*-动力系统（A，α，R），作用在不动点代数的迹泛函的巴拿赫空间上的可逆算子s是正则联系的. KMS态对应于s的正本征向量。Perron-Frobenius型定理断言KMS态的存在温度与s的内、外光谱半径的倒数相等（极值KMS态）。讨论了符号动力学中的子移位、分形几何中的自相似集和非交换度量空间中的子移位的例子。某些子位移自然地与系统相关联，并给出了它们的拓扑熵与极端KMS态的逆温度之间的关系。非交换移位映射被认为是。结果表明，它们的熵是有界的相关子移位的熵和一个适当的熵计算的齐次子代数。举例讨论了与某些非有限型子移位相关的Matsumoto代数。将CNT熵与子移位的经典测量理论熵进行比较。对于某些Matsumoto代数的非交换移位，得到了子移位熵的经典变分原理的一个非交换类似结果。更一般地，讨论了一个必要条件。在Cuntz-Krieger代数的情况下，从唯一的KMS态明确地构造了具有最大熵的态。
We consider a family of $*$-commuting local homeomorphisms on a compact space, and build a compactly aligned product system of Hilbert bimodules (in the sense of Fowler). This product system has a Nica-Toeplitz algebra and a Cuntz-Pimsner algebra. Both algebras carry a gauge action of a higher-dimensional torus, and there are many possible dynamics obtained by composing with different embeddings of the real line in this torus. We study the KMS states of these dynamics. For large inverse temperatures, we describe the simplex of KMS states on the Nica-Toeplitz algebra. To study KMS states for sm…
KMS states on quantum Cuntz-Krieger algebras
本文研究量子图相关的局部量子 Cuntz-Krieger 代数上的 KMS 态，利用与 Cuntz-Pimsner 代数的同构，将 KMS 态判据转化为关于量子邻接算子的命题，并实现了规范作用下 KMS 态的完全分类。
It is shown that any bundle of KMS state spaces which can occur for a flow on a unital separable C*-algebra with a trace state can also be realized by a flow on any given unital infinite-dimensional simple AF algebra with a tracial state space affinely homeomorphic to the fiber in the bundle over 0.
We determine the factor types of the extremal KMS weights for generalized gauge actions on a graph algebra, and the ground states for the restriction of the action to a corner defined from a vertex. The assumptions on the graph and the action varies a bit, but they all cover, at the very least, the case of the gauge action on a strongly connected graph with at most countably many exits. These are the graphs for which all the KMS weights of the gauge action were determined in the first part of this work.
Invariance of KMS states on graph C*-algebras under classical and quantum symmetry
本文研究图C*-代数上KMS态在经典和量子对称下的不变性，证明强连通图的唯一KMS态在量子自守群作用下保持不变，并探讨循环图中不同KMS态的对称性行为。
KMS states for generalized gauge actions on Cuntz-Krieger algebras (An application of the Ruelle-Perron-Frobenius Theorem)
给定一个0 - 1矩阵A，我们考虑Cuntz-Krieger代数O_A的某些单参数自同构群，推广了通常的规范群，并依赖于定义在Markov空间O_A上的正连续函数H.主要结果包括Ruelle的Perron Frobenius定理的应用，以表明这些自同构群承认一个单一的KMS状态。
KMS states on the C*-algebras of reducible graphs
本文研究有限图的C* 代数上的动力学问题，它是通过将规范作用提升为实直线的作用而得到的。Enomoto，Fujii和Watatani证明了如果图的顶点矩阵是不可约的，则图代数上的动力学允许单个KMS状态。我们以前研究了Toeplitz代数上的动力学，并明确地描述了一个有限维的KMS态的单形为反温度高于临界值。本文研究了顶点矩阵可约图的KMS态，以及逆温度在临界值及以下的KMS态。我们证明了一个一般性的结果，它描述了所有的KMS状态在一个固定的反温度，然后应用这个定理的各种例子。我们发现，可以有许多模式的相变，这取决于在底层图形中的路径的行为。
We obtain three results: 1) Every compact simplex bundle with exactly one point in the fiber over 0 is the KMS bundle of a periodic flow on the Jiang-Su algebra. 2) Let A be a separable unital C*-algebra with a unique trace state. Suppose that A tensorially absorbs the Jiang-Su algebra. The (weak) cocycle-conjugacy classes of flows that are not approximately inner are uncountable. 3) Let B be a separable, simple, unital, purely infinite and nuclear C*-algebra in the UCT class. Assume that the K1 group of B is torsion free. Every proper simplex bundle with empty fiber over 0 is the KMS bundle o…
KMS states of quasi-free dynamics on Pimsner algebras
本研究刻画了右希尔伯特C*-双模上连续单参数酉等距群诱导的拟自由动力学的KMS态，推广了此前Cuntz代数等的相关结果，还给出了非酉等距情形下基于KMS权的一般刻画。
KMS states for the generalized gauge action on graph algebras
给定任意有向图$E=(E^0,E^1)$的边集上的一个正函数，在图$C^*(E)$的C* 代数上定义了一个单参数自同构群，并研究了求该作用的KMS态的问题.证明了$C^*(E)$上的KMS态、核上的某类态和$C_0(E^0)$上的某类迹态之间存在双射对应。我们还找到了这种作用的基态，并给出了一些例子。
The relative graph $C^*$-algebras introduced by Muhly and Tomforde are generalizations of both graph algebras and their Toeplitz extensions. For an arbitrary graph $E$ and a subset $R$ of the set of regular vertices of $E$ we show that the relative graph $C^*$-algebra $C^*(E, R)$ is isomorphic to a partial crossed product for an action of the free group generated by the edge set on the relative boundary path space. Given a time evolution on $C^*(E, R)$ induced by a function on the edge set, we characterize the KMS$_β$ states and ground states using an abstract result of Exel and Laca. Guided b…
KMS states on $C^*$-algebras associated to higher-rank graphs
考虑秩为k的高阶图。图的Cuntz-Krieger代数和Toeplitz-Cuntz-Krieger代数都带有环面T^k的自然规范作用量，并且将这些规范作用量限制到T^k的单参数子群，给出了包含实数线作用量的动力系统。我们研究了这些动力系统的KMS态。我们发现，当逆温度β较大时，Toeplitz-Cuntz-Krieger代数上KMS_β态的单形的维数d比图的顶点数小小于1.当β大于β c时，存在一个d维KMS态单形;当β=β c且单参数子群稠密时，存在一个唯一的KMS态，并且这个态通过Cuntz-Krieger代数分解.与以前k=1的研究一样，我们的主要工具是不可约非负矩阵的Perron-Frobenius理论，尽管这里我们需要交换矩阵族的理论版本。
Sheaves of Measures and KMS-Weights on Topological Graph Algebras
本文证明正则博雷尔测度构成层，并利用该结构描述拓扑图C*-代数上规范作用的KMS-权，以顶点空间上的次不变测度刻画。
The paper develops a series of tools for the study of KMS-weights on graph C*-algebras and KMS states on their corners. The approach adopts methods and ideas from graph theory, random walks and dynamical systems.
KMS states on the C*-algebras of non-principal groupoids
本研究借助迷向群C*-代数上迹的可测场刻画平展广群C*-代数的KMS态，将其用于分析变换广群C*-代数的迹态，并为数域ax+b半群Toeplitz代数的已有结果给出简短证明。
We study the equilibrium or KMS states of the Toeplitz C*-algebra of a finite higher-rank graph which is reducible. The Toeplitz algebra carries a gauge action of a higher-dimensional torus, and a dynamics arises by choosing an embedding of the real numbers in the torus. Here we use an embedding which leads to a dynamics which has previously been identified as "preferred", and we scale the dynamics so that 1 is a critical inverse temperature. As with 1-graphs, we study the strongly connected components of the vertices of the graph. The behaviour of the KMS states depends on both the graphical …
KMS states on Nica-Toeplitz algebras of product systems
研究了Hilbert双模半群$P$上紧对齐乘积系统$X$的Fowler Nica-Toeplitz代数$\mathcal{NT}(X)$的KMS态.这种分析依赖于这些状态的核心代数，满足适当的缩放条件的限制。引入了有限型乘积系统的概念。若$(G, P)$是格序群，$X$是$P$上满足某些相干性质的有限型乘积系统，我们利用乘积系统系数代数上的迹构造了与标量动力学相关的$\NT(X)$的KMS $_β$态.我们的结果是受Laca和Raeburn关于自然数上仿射半群的Toeplitz代数的一些结果的启发而得到的，并推广了这些结果.
Given a topologically free action of a countable group $G$ on a compact metric space $X$, there is a canonical correspondence between continuous 1-cocycles for this group action and diagonal 1-parameter groups of automorphisms of the reduced crossed product C*-algebra. The KMS spectrum is defined as the set of inverse temperatures for which there exists a KMS state. We prove that the possible KMS spectra depend heavily on the nature of the acting group $G$. For groups of subexponential growth, we prove that the only possible KMS spectra are $\{0\}$, $[0,+\infty)$, $(-\infty,0]$ and $\mathbb{R}…
We consider self-similar actions of groupoids on the path spaces of finite directed graphs, and construct examples of such self-similar actions using a suitable notion of graph automaton. Self-similar groupoid actions have a Cuntz-Pimsner algebra and a Toeplitz algebra, both of which carry natural dynamics lifted from the gauge actions. We study the equilibrium states (the KMS states) on the resulting dynamical systems. Above a critical inverse temperature, the KMS states on the Toeplitz algebra are parametrised by the traces on the full $C^*$-algebra of the groupoid, and we describe a program…
Several authors have recently been studying the equilibrium or KMS states on the Toeplitz algebras of finite higher-rank graphs. For graphs of rank one (that is, for ordinary directed graphs), there is a natural dynamics obtained by lifting the gauge action of the circle to an action of the real line. The algebras of higher-rank graphs carry a gauge action of a higher-dimensional torus, and there are many potential dynamics arising from different embeddings of the real line in the torus. Previous results show that there is nonetheless a "preferred dynamics" for which the system exhibits a part…
We study the internal structure of $C^*$-algebras of right LCM monoids by means of isolating the core semigroup $C^*$-algebra as the coefficient algebra of a Fock-type module on which the full semigroup $C^*$-algebra admits a left action. If the semigroup has a generalised scale, we classify the KMS-states for the associated time evolution on the semigroup $C^*$-algebra, and provide sufficient conditions for uniqueness of the KMS$_β$-state at inverse temperature $β$ in a critical interval.
KMS states on uniform Roe algebras
本文研究一致Roe代数上一类自然流的KMS态，证明其通过对角算子分解，并揭示了强连续态的唯一性及其与Higson冠的联系，最后应用于$n$-分支树。
The paper contains a description of the KMS states and ground states of a generalized gauge action on the C*-algebra of a finite graph.
We study the generalised Bunce-Deddens algebras and their Toeplitz extensions constructed by Kribs and Solel from a directed graph and a sequence $ω$ of positive integers. We describe both of these $C^*$-algebras in terms of novel universal properties, and prove uniqueness theorems for them; if $ω$ determines an infinite supernatural number, then no aperiodicity hypothesis is needed in our uniqueness theorem for the generalised Bunce-Deddens algebra. We calculate the KMS states for the gauge action in the Toeplitz algebra when the underlying graph is finite. We deduce that the generalised Bunc…
Five shades of KMS: Statistical properties in the spectral geometry of Cuntz--Krieger algebras
本文研究拓扑马尔可夫链和Cuntz-Krieger代数的非交换几何中的谱不变量，通过log-Laplacian构建的谱三元组证明了统计特征值渐近、局部热迹渐近、局部Weyl定律以及Connes迹定理的类比，所有局部渐近由Cuntz-Krieger代数上规范作用的Kubo-Martin-Schwinger态控制。
The Toeplitz algebra $\mathcal{T}C^{*}(Λ)$ for a finite $k$-graph $Λ$ is equipped with a continuous one-parameter group $α^{r}$ for each $ r\in \mathbb{R}^{k}$, obtained by composing the map $\mathbb{R} \ni t \to (e^{itr_{1}}, \dots , e^{itr_{k}}) \in \mathbb{T}^{k}$ with the gauge action on $\mathcal{T}C^{*}(Λ)$. In this paper we give a complete description of the $β$-KMS states for the $C^{*}$-dynamical system $(\mathcal{T}C^{*}(Λ), α^{r})$ for all finite $k$-graphs $Λ$ and all values of $β\in \mathbb{R}$ and $r\in \mathbb{R}^{k}$.
We study some relations between self-similar group actions and operator algebras. We consider KMS states on the Cuntz--Pimsner algebras constructed by Nekrashevych from self-similar actions and the GNS representations of the KMS states. The KMS states are given by the Bernoulli measure. We also consider the von Neumann algebras on the GNS spaces and show that the von Neumann algebras are type III factors.
An introduction to KMS weights
本文系统介绍KMS权重理论，以低预备门槛证明核心定理，并结合von Neumann代数模理论梳理经典与作者的最新成果及因子类型。
KMS states on $\mathbb{Z}_2$-crossed products and twisted KMS functionals
本文刻画了$\mathbb{Z}_2$-交叉积上的KMS态，通过扭曲KMS泛函描述其扩张，并分析了CAR代数情形，应用于Ising QFT的扩展场代数。
The Toeplitz algebra of a finite graph of rank $k$ carries a natural action of the torus ${\mathbb T}^k$, and composing with an embedding of ${\mathbb R}$ in ${\mathbb T}^k$ gives a dynamics on the Toeplitz algebra. For inverse temperatures larger than a critical value, the KMS states for this dynamics are well-understood, and this analysis is the first step in our program. At the critical inverse temperature, much less is known, and the second step in our program is an analysis of the KMS states at the critical value. This is the main technical contribution of the present paper. The third ste…
Let $G$ be a countable discrete amenable group, and $Λ$ be a strongly connected finite $k$-graph. If $(G,Λ)$ is a pseudo free and locally faithful self-similar action which satisfies the finite-state condition, then the structure of the KMS simplex of the C*-algebra $Ø_{G,Λ}$ associated to $(G,Λ)$ is described: it is either empty or affinely isomorphic to the tracial state space of the C*-algebra of the periodicity group $\Per_{G,Λ}$ of $(G,Λ)$, depending on whether the Perron-Frobenius eigenvector of $Λ$ preserves the $G$-action. As applications of our main results, we also exhibit several cl…
Exact circle maps and KMS states
本文描述了圆的连续分段单调精确映射的定向变换广群的C* 代数上规范作用量的KMS态和基态。
The admissible KMS bundles on classifiable C$^*$-algebras
本文证明了在可分类 C$^*$-代数和 UCT Kirchberg 代数上，对于满足特定拓扑条件的单纯形丛，均存在实现该单纯形的流。
Let $φ:X\to X$ be a homeomorphism of a compact metric space $X$. For any continuous function $F:X\to \mathbb{R}$ there is a one-parameter group $α^{F}$ of automorphisms on the crossed product $C^*$-algebra $C(X)\rtimes_φ\mathbb{Z}$ defined such that $α^{F}_{t}(fU)=fUe^{-itF}$ when $f \in C(X)$ and $U$ is the canonical unitary in the construction of the crossed product. In this paper we study the KMS states for these flows by developing an intimate relation to the ergodic theory of non-singular transformations and show that the structure of KMS-states can be very rich and complicated. Our resul…
Families of Type {\rm III KMS} States on a Class of $C^*$-Algebras containing $O_n$ and $\mathcal{Q}_\N$
我们构造了一族纯无限$C^*$ -代数，$\mathcal{Q}^λ$ for $λ\in (0,1)$，并按它们的$K$ -群进行分类。在每个$\mathcal{Q}^λ.$上有一个具有唯一${\rm KMS}$状态$ψ$的圆$\T$的动作对于$λ=1/n,$ $\mathcal{Q}^{1/n}\cong O_n$，具有其通常的$\T$动作和${\rm KMS}$状态。对于最低项的$λ=p/q,$有理数，$\mathcal{Q}^λ\cong O_n$（$n=q-p+1$）具有$(pq)^\infty.$类型的UHF不动点代数对于任何$n>0,$ $\mathcal{Q}^λ\cong O_n$，对于无限多个具有不同KMS状态的$λ$和UHF不动点代数。对于任何$λ\in (0,1),$ $\mathcal{Q}^λ\neq O_\infty.$对于$λ$无理的不动点代数，不是AF和$\mathcal{Q}^λ$通常不是Cuntz代数。对于$λ$先验的，$K_1\cong K_0\cong\Z^\infty$，所以$\mathcal{Q}^λ$是Cuntz的$\mathcal Q_{\N}$，\cite{Cu1}。如果$λ^{\pm 1}$都是代数整数，则出现的{ \bf only} $O_n$满足$n\equiv 3(mod 4).$对于每个$λ$，由KMS状态$ψ$定义的$…
We construct KMS-states from $\mathrm{Li}_1$-summable semifinite spectral triples and show that in several important examples the construction coincides with well-known direct constructions of KMS-states for naturally defined flows. Under further summability assumptions the constructed KMS-state can be computed in terms of Dixmier traces. For closed manifolds, we recover the ordinary Lebesgue integral. For Cuntz-Pimsner algebras with their gauge flow, the construction produces KMS-states from traces on the coefficient algebra and recovers the Laca-Neshveyev correspondence. For a discrete group…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。