Related papers: KMS weights on groupoid and graph C*-algebras

We introduce the notion of a C*-valued weight between two C*-algebras as a generalization of an ordinary weight on a C*-algebra and as a C*-version of operator valued weights on von Neumann algebras. Also, some form of lower semi-continuity…

It shown that an a locally injective surjection on a compact metric space admits a canonical locally homeomorphic extension such that the associated C*-algebras are isomorphic. This is then used in a study of the possible inverse…

We explore the recently introduced local-triviality dimensions by studying gauge actions on graph $C^*$-algebras, as well as the restrictions of the gauge action to finite cyclic subgroups. For $C^*$-algebras of finite acyclic graphs and…

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…

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…

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…

Inspired by Franks' classification of irreducible shifts of finite type we provide a short list of allowed moves on graphs that preserves the stable isomorphism class of the associated C*-algebras. We show that if two graphs have stably…

In this paper, we introduce the notion of a dual topological graph of a given topological graph, and show that it defines a C*-algebra isomorphic to the C*-algebra of the given one. Repeating to take a dual, and taking a projective limit,…

Topological quivers are generalizations of directed graphs in which the sets of vertices and edges are locally compact Hausdorff spaces. Associated to such a topological quiver Q is a C*-correspondence, and from this correspondence one may…

The reduced $C^*$-algebra of the interior of the isotropy in any Hausdorff \'etale groupoid $G$ embeds as a $C^*$-subalgebra $M$ of the reduced $C^*$-algebra of $G$. We prove that the set of pure states of $M$ with unique extension is…

We extend theorems of Breuillard-Kalantar-Kennedy-Ozawa on unital reduced crossed products to the non-unital case under mild assumptions. As a result simplicity of C*-algebras is stable under taking reduced crossed product over discrete…

We prove the uniqueness, up to a pull-back by an element of a suitable subgroup of complex automorphisms, of the weighted extremal K\"ahler metrics on a compact K\"ahler manifold introduced in our previous work. This extends a result by…

We prove that for every exact discrete group $\Gamma$, there is an intermediate C*-algebra between the reduced group C*-algebra and the intersection of the group von Neumann algebra and the uniform Roe algebra which is realized as the…

We introduce an algebraic version of the Katsura $C^*$-algebra of a pair $A,B$ of integer matrices and an algebraic version of the Exel-Pardo $C^*$-algebra of a self-similar action on a graph. We prove a Graded Uniqueness Theorem for such…

In this paper we generalize the notion of a $k$-graph into (countable) infinite rank. We then define our $C^*$-algebra in a similar way as in $k$-graph $C^*$-algebras. With this construction we are able to find analogues to the Gauge…

We study graph $C^*$-algebras equipped with generalised gauge actions, and characterise in terms of groupoids and groupoid cocycles when two graph $C^*$-algebras are isomorphic by a diagonal-preserving isomorphism that intertwines the…

We consider the boundary-path groupoids of topological higher-rank graphs. We show that the all such groupoids are topologically amenable. We deduce that the C*-algebras of topological higher-rank graphs are nuclear and prove versions of…

We completely classify the atomic summands in a graph product $(M,\varphi) = *_{v \in \mathcal{G}} (M_v,\varphi_v)$ of von Neumann algebras with faithful normal states. Each type I factor summand $(N,\psi)$ is a tensor product of type I…

We consider a locally compact Hausdorff groupoid $G$, and twist by a more general locally compact Hausdorff abelian group $\Gamma$ rather than the complex unit circle $\mathbb{T}$. We investigate the construction of $C^*$-algebras in…

This article extends the main results of the publication arXiv:2001.01312 to the case of a twisted groupoid. More precisely, it gives a decomposition of the C*-algebra of a twisted locally compact groupoid with Haar system in presence of a…