Related papers: Examples of masas in C*-algebras

Let A be a C*-algebra and d from A into A** be a continuous linear map. We assume that d acts like derivation or anti-derivation at orthogonal elements for several types of orthogonality conditions such as ab=0, ab*=0, ab=ba=0 and…

For an inclusion of C*-algebras $D\subseteq A$ with $D$ abelian, we show that when $n\in A$ normalizes $D$, $n^*n$ and $nn^*$ commute with $D$. As a corollary, when $D$ is a regular MASA in $A$, every approximate unit for $D$ is also an…

In this paper, we initiate the study of higher rank Baumslag-Solitar semigroups and their related C*-algebras. We focus on two extreme, but interesting, classes - one is related to products of odometers and the other is related to…

Motivated by Exel's inverse semigroup approach to combinatorial C*-algebras, in a previous work the authors defined an inverse semigroup associated with a labelled space. We construct a representation of the C*-algebra of a labelled space,…

We characterise Exel's noncommutative Cartan subalgebras in several ways using uniqueness of conditional expectations, relative commutants, or purely outer inverse semigroup actions. We describe in which sense the crossed product…

The cone of lower semicontinuous traces is studied with a view to its use as an invariant. Its properties include compactness, Hausdorffness, and continuity with respect to inductive limits. A suitable notion of dual cone is given. The cone…

It is proved some results about existence and non existence of unit normal sections of submanifolds of the Euclidean space and sphere which associated Gauss maps are harmonic. Some applications to CMC hypersurfaces of the sphere and…

For a large class of finite graphs $E$, we show that whenever $\alpha$ is a vertex-fixing quasi-free automorphism of the corresponding graph $C^*$-algebra $C^*(E)$ such that $\alpha({\mathcal D}_E) \neq{\mathcal D}_E$, where ${\mathcal…

We introduce a classification of locally compact Hausdorff topological spaces with respect to the behavior of $\sigma$-compact subsets, and relying on this classification we study properties of corresponding $C^*$-algebras in terms of frame…

In this paper, two sufficient and necessary conditions are given. The first one characterizes when the boundary path groupoid of a topological graph without singular vertices has closed interior of its isotropy group bundle, and the second…

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…

Let $R$ be a rational function. The iterations $(R^n)_n$ of $R$ gives a complex dynamical system on the Riemann sphere. We associate a $C^*$-algebra and study a relation between the $C^*$-algebra and the original complex dynamical system.…

We study Cartan-Subalgebras of Lie-Algebras associated to associative algebras.

C*-algebras are widely used in mathematical physics to represent the observables of physical systems, and are sometimes taken as the starting point for rigorous formulations of quantum mechanics and classical statistical mechanics.…

We construct ample groupoids from certain categories of paths, and prove that their $C^*$-algebras coincide with the continued fraction AF algebras of Effros and Shen. The proof relies on recent classification results for simple nuclear…

This is the first of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we define the maps in the more general context of orbispaces, and establish several basic results concerning the…

Renault proved in 2008 that if $G$ is a topologically principal groupoid, then $C_0(G^{(0)})$ is a Cartan subalgebra in $C^*_r(G, \Sigma)$ for any twist $\Sigma$ over $G$. However, there are many groupoids which are not topologically…

We introduce the notion of continuous orbit equivalence for partial dynamical systems, and give an equivalent characterization in terms of Cartan-isomorphisms for partial C*-crossed products. Both graph C*-algebras and semigroup C*-algebras…

We study analogues of the radial subalgebras in free group factors (called the algebras of class functions) in the setting of compact quantum groups. For the free orthogonal quantum groups we show that they are not MASAs, as soon as we are…

Let $R$ be a rational function with degree $\geq 2$ and $X$ be its Julia set, its Fatou set, or the Riemann sphere. Suppose that $X$ is not empty. We can regard $R$ as a continuous map from $X$ onto itself. Kajiwara and Watatani showed that…