Related papers: C*-algebras of commuting endomorphisms

We study the ideal structure of $C^*$-algebras arising from $C^*$-correspondences. We prove that gauge-invariant ideals of our $C^*$-algebras are parameterized by certain pairs of ideals of original $C^*$-algebras. We show that our…

This paper is a continuation of the paper entitled "Subshifts, $\lambda$-graph bisystems and $C^*$-algebras", arXiv:1904.06464. A $\lambda$-graph bisystem consists of a pair of two labeled Bratteli diagrams satisfying certain compatibility…

Given a semigroup of local homeomorphisms on a compact space X we consider the corresponding semigroup of *-endomorphisms on C(X) and discuss the possibility of extending it to an interaction group, a concept recently introduced by the…

We compute the two-cocycles (or multipliers) of the free nilpotent groups of class $2$ and rank $n$ and give conditions for simplicity of the corresponding twisted group $C^*$-algebras. These groups are representation groups for…

In this paper we describe the C*-algebras associated to the Baumslag-Solitar groups with the ordering defined by the usual presentations. These are Morita equivalent to the crossed product C*-algebras obtained by letting the group act on…

Let $K$ be a compact metric space and let $\varphi: K \to K$ be continuous. We study C*-algebra $\mathcal{MC}_\varphi$ generated by all multiplication operators by continuous functions on $K$ and a composition operator $C_\varphi$ induced…

We show that the method to construct C^*-algebras from topological graphs, introduced in our previous paper, generalizes many known constructions. We give many ways to make new topological graphs from old ones, and study the relation of…

Gelfand duality between unital commutative C*-algebras and Compact Hausdorff spaces is extended to all unital C*-algebras, where the dual objects are what we call compact Hausdorff quantum spaces. We apply this result to obtain, a…

We study strong compactly aligned product systems of $\mathbb{Z}_+^N$ over a C*-algebra $A$. We provide a description of their Cuntz-Nica-Pimsner algebra in terms of tractable relations coming from ideals of $A$. This approach encompasses…

C*-bundle dynamical systems are introduced and their r\^ole within the theory of C*-subalgebras and Fell bundles is investigated. A C*-bundle dynamical system involves an action of a 1-parameter group of "spatial automorphisms" of the…

We introduce a new method of expressing a $k$-graph $C^*$-algebra as a Cuntz-Pimsner algebra. Kumjian, Pask, and Sims have done this directly, using a linking algebra approach and a $(k-1)$-graph algebra. This can be iterated downward. Our…

We study the categorical homology of Zappa-Sz\'ep products of small categories, which include all self-similar actions. We prove that the categorical homology coincides with the homology of a double complex, and so can be computed via a…

Let $\mathbb{G}$ be a locally compact quantum group, and $A,B$ von Neumann algebras on which $\mathbb{G}$ acts. We refer to these as $\mathbb{G}$-dynamical W$^*$-algebras. We make a study of $\mathbb{G}$-equivariant $A$-$B$-correspondences,…

C*-algebras form rather general and rich mathematical structures that can be studied with different morphisms (preserving multiplication, or not), and with different properties (commutative, or not). These various options can be used to…

We define and systematically study nonassociative C*-algebras as C*-algebras internal to a topological tensor category. We also offer a concrete approach to these C*-algebras, as G-invariant, norm closed *-subalgebras of bounded operators…

We associate a $C^*$-algebra to a partial action of the integers acting on the base space of a vector bundle, using the framework of Cuntz--Pimsner algebras. We investigate the structure of the fixed point algebra under the canonical gauge…

In this paper, we initiate the study of endomorphisms and modular theory of the graph C*-algebras $\O_{\theta}$of a 2-graph $\Fth$ on a single vertex. We prove that there is a semigroup isomorphism between unital endomorphisms of…

In this paper we analyse the structure of the Cuntz semigroup of certain $C(X)$-algebras, for compact spaces of low dimension, that have no $\mathrm{K}_1$-obstruction in their fibres in a strong sense. The techniques developed yield…

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 introduce a family of $C^*$-correspondences $X_\alpha$ naturally associated to every ordinal graph $\Lambda$. When $\Lambda$ is a directed graph, $X_0$ is isomorphic to the usual $C^*$-correspondence associated to a graph. We show that…