Related papers: KMS quantum symmetric states
We give a notion of quantum automorphism group of graph C*-algebras without sink at critical inverse temperature. This is defined to be the universal object of a category of CQG's having a linear action in the sense of [11] and preserving…
We study invariance of KMS states on graph C*-algebras coming from strongly connected and circulant graphs under the classical and quantum symmetry of the graphs. We show that the unique KMS state for strongly connected graphs is invariant…
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…
Let $\varphi:X\to X$ be a homeomorphism of a compact metric space $X$. For any continuous function $F:X\to \mathbb{R}$ there is a one-parameter group $\alpha^{F}$ of automorphisms on the crossed product $C^*$-algebra…
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…
Let $G$ be a countable discrete amenable group, and $\Lambda$ be a strongly connected finite $k$-graph. If $(G,\Lambda)$ is a pseudo free and locally faithful self-similar action which satisfies the finite-state condition, then the…
We compute all the quantum symmetries of a graph with n- disjoint loops at the critical inverse temperature. We show that the set of non-isomorphic CQG's appearing as quantum symmetry at the critical inverse temperature has a one to one…
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 show that the space of tracial quantum symmetric states of an arbitrary unital C*-algebra is a Choquet simplex and is a face of the tracial state space of the universal unital C*-algebra free product of A with itself infinitely many…
To any periodic, unital and full C*-dynamical system (A, \alpha, 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…
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…
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 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…
Given a right LCM semigroup $S$ and a homomorphism $N\colon S\to[1,+\infty)$, we use the groupoid approach to study the KMS$_\beta$-states on $C^*(S)$ with respect to the dynamics induced by $N$. We establish necessary and sufficient…
We consider operator-algebraic dynamical systems given by actions of the real line on unital $C^*$-algebras, and especially the equilibrium states (or KMS states) of such systems. We are particularly interested in systems built from the…
Given a zero-one matrix A we consider certain one-parameter groups of automorphisms of the Cuntz-Krieger algebra O_A, generalizing the usual gauge group, and depending on a positive continuous function H defined on the Markov space…
We introduce symmetric states and quantum symmetric states on universal unital free product C*-algebras an arbitrary unital C*-algebra A with itself infinitely many times, as a generalization of the notions of exchangeable and quantum…
On the example of a free massless and conformally coupled scalar field, it is argued that in quantum field theory in curved spacetimes with time-like Killing field, the corresponding KMS states (generalized Gibbs ensembles) at parameter…
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…
In this paper, we study KMS states for the gauge actions on C${}^*$-algebras associated with self-similar sets whose branch points are finite. If the self-similar set does not contain any branch point, the Hutchinson measure gives the…