Related papers: C*-equivalences of graphs

These notes concern aspects of various graphs whose vertex set is a group $G$ and whose edges reflect group structure in some way (so that they are invariant under the action of the automorphism group of $G$). The graphs I will discuss are…

We classify graph C*-algebras, namely, Cuntz-Krieger algebras associated to the Bass-Hashimoto edge incidence operator of a finite graph. This is done by a purely graph theoretical calculation of the K-theory and the position of the unit…

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,…

We generalise the theory of Cuntz-Krieger families and graph algebras to the class of finitely aligned $k$-graphs. This class contains in particular all row-finite $k$-graphs. The Cuntz-Krieger relations for non-row-finite $k$-graphs look…

Given a locally compact group $G$ and a unitary representation $\rho:G\to U({\mathcal H})$ on a Hilbert space ${\mathcal H}$, we construct a $C^*$-correspondence ${\mathcal E}(\rho)={\mathcal H}\otimes_{\mathbb C} C^*(G)$ over $C^*(G)$ and…

Let $\Lambda = \mathbb{Z}^n$ with lexicographic ordering. $\Lambda$ is a totally ordered group. Let $X = \Lambda^+ * \Lambda^+$. Then $X$ is a $\Lambda$-tree. Analogous to the construction of graph $C^*$-algebras, we form a groupoid whose…

We prove a strong rigidity property of the Heisenberg groups, that is, they can be distinguished from any other 1-connected Lie groups via their unitary dual spaces, in particular via the Morita equivalence class of their group…

We prove that separable C*-algebras which are completely close in a natural uniform sense have isomorphic Cuntz semigroups, continuing a line of research developed by Kadison - Kastler, Christensen, and Khoshkam. This result has several…

We revisit a central result of Muhly and Solel on operator algebras of C*-correspondences. We prove that (possibly non-injective) strongly Morita equivalent C*-correspondences have strongly Morita equivalent relative Cuntz-Pimsner…

We give a classification result for a certain class of $C^{*}$-algebras $\mathfrak{A}$ over a finite topological space $X$ in which there exists an open set $U$ of $X$ such that $U$ separates the finite and infinite subquotients of…

We discuss the relative K-theory for a $C^{*}$-algebra, $A$, together with a $C^{*}$-subalgebra, $A' \subseteq A$. The relative group is denoted $K_{i}(A';A), i = 0, 1$, and is due to Karoubi. We present a situation of two pairs $A'…

We determine the primitive ideal space and hence the ideal lattice of a large class of separable groupoid C*-algebras that includes all 2-graph C*-algebras. A key ingredient is the notion of harmonious families of bisections in etale…

Given a Hausdorff locally compact \'etale groupoid $\mathcal G$, we describe as a topological space the part of the primitive spectrum of $C^*(\mathcal G)$ obtained by inducing one-dimensional representations of amenable isotropy groups of…

In the theory of C*-algebras, the Weyl groups were defined for the Cuntz algebras and graph algebras by Cuntz and Conti et al. respectively. In this paper, we introduce and investigate the Weyl groups of groupoid C*-algebras as a natural…

These are some notes I wrote for the summer school "Symbolic dynamics and homeomorphisms of the Cantor set" at the University of Copenhagen, 23 - 27 June 2008. The notes contain the definition of the C*-algebra associated to a shift space…

We study the C*-algebras of Fell bundles. In particular, we prove the analogue of Renault's disintegration theorem for groupoids. As in the groupoid case, this result is the key step in proving a deep equivalence theorem for the C*-algebras…

Let R be an equivalence relation on graphs. By the strengthening of R we mean the relation R' such that graphs G and H are in the relation R' if for every graph F, the union of the graphs G and F is in the relation R with the union of the…

In this paper, we introduce a notion of a self-similar action of a group $G$ on a $k$-graph $\Lambda$, and associate it a universal C*-algebra $\O_{G,\Lambda}$. We prove that $\O_{G,\Lambda}$ can be realized as the Cuntz-Pimsner algebra of…

We show that two C*-algebraic noncommutative tori are strongly Morita equivalent if and only if they have isomorphic ordered K_0-groups and centers, extending N. C. Phillips's result in the case that the algebras are simple. This is also…

In previous work, we defined and studied $\Sigma^*$-modules, a class of Hilbert $C^*$-modules over $\Sigma^*$-algebras (the latter are $C^*$-algebras that are sequentially closed in the weak operator topology). The present work continues…