相关论文: The groupoid approach to equilibrium states on rig…

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.…

Given a quasi-lattice ordered group $(G,P)$ and a compactly aligned product system $X$ of essential C$^*$-correspondences over the monoid $P$, we show that there is a bijection between the gauge-invariant KMS$_\beta$-states on the…

We compute the KMS (equilibrium) states for the canonical time evolution on C*-algebras from actions of congruence monoids on rings of algebraic integers. We show that for each $\beta\in[1,2]$, there is a unique KMS$_\beta$ state, and we…

Each multiplicative real-valued homomorphism on a quasi-lattice ordered monoid gives rise to a quasi-periodic dynamics on the associated Toeplitz C*-algebra; here we study the KMS equilibrium states of the resulting C*-dynamical system. We…

We examine Nica-Pimsner algebras associated with semigroup actions of $\mathbb{Z}_+^n$ on a C*-algebra $A$ by $*$-endomorphisms. We give necessary and sufficient conditions on the dynamics for exactness and nuclearity of the Nica-Pimsner…

A continuous groupoid homomorphism $c$ on a locally compact second countable Hausdorff \'etale groupoid $\mathcal{G}$ gives rise to a $C^{*}$-dynamical system in which every $\beta$-KMS state can be associated to a $e^{-\beta…

We introduce the notion of a self-similar action of a groupoid $G$ on a finite higher-rank graph. To these actions we associate a compactly aligned product system of Hilbert bimodules, and thereby obtain corresponding universal…

We consider a finite directed graph E, and the gauge action on its Toeplitz-Cuntz-Krieger algebra, viewed as an action of R. For inverse temperatures larger than a critical value \beta_c, we give an explicit construction of all the…

We develop a general framework for analyzing KMS-states on C*-algebras arising from actions of Hecke pairs. We then specialize to the system recently introduced by Connes and Marcolli and classify its KMS-states for inverse temperatures…

We first prove that the subalgebra $\mathcal{C}$ generated by the vertex and face operators of an abelian Kitaev model is a $C^\ast$-diagonal of the UHF algebra $\mathcal{A}$ of quasilocal observables. This gives us access to the Weyl…

The Toeplitz algebra $\mathcal{T}C^{*}(\Lambda)$ for a finite $k$-graph $\Lambda$ is equipped with a continuous one-parameter group $\alpha^{r}$ for each $ r\in \mathbb{R}^{k}$, obtained by composing the map $\mathbb{R} \ni t \to…

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…

We introduce a non-commutative generalization of the notion of (approximately proper) equivalence relation and propose the construction of a "quotient space". We then consider certain one-parameter groups of automorphisms of the resulting…

Given a self-similar $K$ set defined from an iterated function system $\Gamma=(\gamma_1,\ldots,\gamma_n)$ 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…

We determine the structure of equilibrium states for a natural dynamics on the boundary quotient diagram of $C^*$-algebras for a large class of right LCM semigroups. The approach is based on abstract properties of the semigroup and covers…

Consider a higher-rank graph of rank k. Both the Cuntz-Krieger algebra and the Toeplitz-Cuntz-Krieger algebra of the graph carry natural gauge actions of the torus T^k, and restricting these gauge actions to one-parameter subgroups of T^k…

We describe KMS-states on the C*-algebras of etale groupoids in terms of measurable fields of traces on the C*-algebras of the isotropy groups. We use this description to analyze tracial states on the transformation groupoid C*-algebras and…

We study the high-temperature equilibrium for the C*-algebra $\mathcal T (\mathbb N^\times \ltimes \mathbb N)$ recently considered by an Huef, Laca and Raeburn. We show that the simplex of KMS$_\beta$ states at each inverse temperature…

We study KMS states on finite-graph C*-algebras with sinks and sources. We compare finite-graph C*-algebras with C*-algebras associated with complex dynamical systems of rational functions. We show that if the inverse temperature $\beta$ is…

Let $p\colon \mathcal{A} \to G$ be a saturated Fell bundle over a locally compact, Hausdorff, second countable, {\'e}tale groupoid~$G$, and let $\mathrm{C}^*(G;\mathcal{A})$ denote its full $\mathrm{C}^*$-algebra. We prove an…