Related papers: Curious properties of free hypergraph C*-algebras

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…

A surjective endomorphism or, more generally, a polymorphism in the sense of \cite{SV}, of a compact abelian group $H$ induces a transformation of $L^2(H)$. We study the C*-algebra generated by this operator together with the algebra of…

We explore the concept of a graph homomorphism through the lens of C$^*$-algebras and operator systems. We start by studying the various notions of a quantum graph homomorphism and examine how they are related to each other. We then define…

We define and study large and stably large subalgebras of simple unital C*-algebras. The basic example is the orbit breaking subalgebra of a crossed product by Z, as follows. Let X be an infinite compact metric space, let h be a minimal…

We study the structure and compute the stable rank of C*-algebras of finite higher-rank graphs. We completely determine the stable rank of the C*-algebra when the k-graph either contains no cycle with an entrance, or is cofinal. We also…

Given two unital C*-algebras $A$ and $B$, we study, when it exists, the universal unital $C^*$-algebra $\mathcal{U}(A,B)$ generated by the coefficients of a unital $*$-homomorphism $\rho\,:\, A\rightarrow B\otimes\mathcal{U}(A,B)$. When $B$…

We discuss just infiniteness of C*-algebras associated to discrete quantum groups and relate it to the C*-uniqueness of the quantum groups in question, i.e. to the uniqueness of a C*-completion of the underlying Hopf *-algebra. It is shown…

A graph $G$ is $H$-free if it does not contain an induced subgraph isomorphic to $H$. The study of the typical structure of $H$-free graphs was initiated by Erd\H{o}s, Kleitman and Rothschild, who have shown that almost all $C_3$-free…

Let $G$ be a finite group and $H$ a normal subgroup. $D(H;G)$ is the crossed product of $C(H)$ and ${\Bbb C}G$ which is only a subalgebra of $D(G)$, the quantum double of $G$. One can construct a $C^*$-subalgebra ${\mathcal{F}}_{_H}$ of the…

Within the framework of free actions of compact quantum groups on unital C*-algebras, we propose two conjectures. The first one states that, if $H$ is the C*-algebra of a compact quantum group coacting freely on a unital C*-algebra $A$,…

In this work we construct a C*-algebra from an injective endomorphisms of some group G, allowing the endomorphism to have infinite cokernel. We generalize results obtained by I. Hirshberg and also by J. Cuntz and A. Vershik. In good cases…

Let $\mathcal{G}$ be an ultragraph and let $C^*(\mathcal{G})$ be the associated $C^*$-algebra introduced by Mark Tomforde. For any gauge invariant ideal $I_{(H,B)}$ of $C^*(\mathcal{G})$, we analyze the structure of the quotient…

For a locally compact group G and a compact subgroup K, the corresponding Hecke algebra consists of all continuous compactly supported complex functions on G that are K-bi-invariant. There are many examples of totally disconnected locally…

We find a substantial class of pairs of $*$-homomorphisms between graph C*-algebras of the form $C^*(E)\hookrightarrow C^*(G)\twoheadleftarrow C^*(F)$ whose pullback C*-algebra is an AF graph C*-algebra. Our result can be interpreted as a…

The independence number $\alpha(H)$ of a hypergraph $H$ is the maximum cardinality of a set of vertices of $H$ that does not contain an edge of $H$. Generalizing Shearer's classical lower bound on the independence number of triangle-free…

Motivated by classical facts concerning closed manifolds, we introduce a strong finiteness property in K-homology. We say that a C*-algebra has uniformly summable K-homology if all its K-homology classes can be represented by Fredholm…

Examples of (strongly continuous) one-parameter groups of automorphisms of UHF C*-algebras are given. One example has the property that the infinitesimal generator does not have a union of finite-dimensional subalgebras as a core. (This…

We study semiprojective, subhomogeneous C*-algebras and give a detailed description of their structure. In particular, we find two characterizations of semiprojectivity for subhomogeneous C*-algebras: one in terms of their primitive ideal…

We begin with the characterization of quantum graphs as left ideals in $\mathcal M \otimes_{eh} \mathcal M$ (the extended Haagerup tensor product of $\mathcal M$ with itself) to avoid technicalities surrounding representation dependence of…

A notion of unique ergodicity relative to the fixed-point subalgebra is defined for automorphisms of unital C*-algebras. It is proved that the free shift on any reduced amalgamated free product C*-algebra is uniquely ergodic relative to its…