相关论文: Supercritical phase transition on the Toeplitz alg…

Spielberg has recently shown that Baumslag-Solitar groups associated to pairs of positive integers are quasi-lattice ordered in the sense of Nica. Thus they have tractable Toeplitz algebras. Each of these algebras carries a natural…

We show that the group ${\mathbb Q \rtimes \mathbb Q^*_+}$ of orientation-preserving affine transformations of the rational numbers is quasi-lattice ordered by its subsemigroup ${\mathbb N \rtimes \mathbb N^\times}$. The associated Toeplitz…

We complete the analysis of KMS-states of the Toeplitz algebra of the affine semigroup over the natural numbers, recently studied by Raeburn and the first author, by showing that for every inverse temperature beta in the critical interval…

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…

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…

Given a countably infinite 0-1 matrix A without identically zero rows, let O_A be the Cuntz-Krieger algebra recently introduced by the authors and T_A be the Toeplitz extension of O_A, once the latter is seen as a Cuntz-Pimsner algebra, as…

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 exhibit a one-parameter group of automorphism on the Cuntz-algebra O_2 such that the simplex of KMS states changes abruptly at a certain critical temperature from infinitely many to one, and then none. The factor types of the extremal…

We describe a construction which associates to any function field $k$ and any place $\infty$ of $k$ a $C^*$-dynamical system $(C_{k,\infty},\sigma_t)$ that is analogous to the Bost-Connes system associated to $\QQ$ and its archimedian…

We associate a canonical Hecke pair of semidirect product groups to the ring inclusion of the algebraic integers $\oo$ in a number field $\kk$, and we construct a C*-dynamical system on the corresponding Hecke C*-algebra, analogous to the…

We study the equilibrium simplex of Nica-Pimsner algebras arising from product systems of finite rank on the free abelian semigroup. First we show that every equilibrium state has a convex decomposition into parts parametrized by ideals on…

We consider a family of Cuntz-Pimsner algebras associated to self-similar group actions, and their Toeplitz analogues. Both families carry natural dynamics implemented by automorphic actions of the real line, and we investigate the…

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…

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…

For every Hilbert bimodule over a C*-algebra, there are natural gauge actions of the circle on the associated Toeplitz algebra and Cuntz-Pimsner algebra, and hence natural dynamics obtained by lifting these gauge actions to actions of the…

In recent work, Cuntz, Deninger and Laca have studied the Toeplitz type C*-algebra associated to the affine monoid of algebraic integers in a number field, under a time evolution determined by the absolute norm. The KMS equilibrium states…

We associate with the ring $R$ of algebraic integers in a number field a C*-algebra $\cT[R]$. It is an extension of the ring C*-algebra $\cA[R]$ studied previously by the first named author in collaboration with X.Li. In contrast to…

An integer matrix $A\in M_d(\Z)$ induces a covering $\sigma_A$ of $\T^d$ and an endomorphism $\alpha_A:f\mapsto f\circ \sigma_A$ of $C(\T^d)$ for which there is a natural transfer operator $L$. In this paper, we compute the KMS states on…

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…

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…