Related papers: Traces on Topological Graph Algebras
The construction of the C*-algebra associated to a directed graph $E$ is extended to incorporate a family $C$ consisting of partitions of the sets of edges emanating from the vertices of $E$. These C*-algebras $C^*(E,C)$ are analyzed in…
We propose a practical computational framework for detecting structural changes in parameter-dependent topological data. In many applications, such as time-series data analysis, anomaly detection, and monitoring of systems under changing…
Various subsets of the tracial state space of a unital C*-algebra are studied. The largest of these subsets has a natural interpretation as the space of invariant means. II_1-factor representations of a class of C*-algebras considered by…
We study dimension theory for the $C^*$-algebras of row-finite $k$-graphs with no sources. We establish that strong aperiodicity - the higher-rank analogue of condition (K) - for a $k$-graph is necessary and sufficient for the associated…
If $R$ is a commutative ring, $M$ a compact $R$-oriented manifold and $G$ a finite graph without loops or multiple edges, we consider the graph configuration space $M^G$ and a Bendersky-Gitler type spectral sequence converging to the…
We introduce a revised notion of gauge action in relation with Leavitt path algebras. This notion is based on group schemes and captures the full information of the grading on the algebra as it is the case of the gauge action of the graph…
Let a compact Lie group act ergodically on a unital $C^*$-algebra $A$. We consider several ways of using this structure to define metrics on the state space of $A$. These ways involve length functions, norms on the Lie algebra, and Dirac…
We provide a complete invariant for graph C*-algebras which are amplified in the sense that whenever there is an edge between two vertices, there are infinitely many. The invariant used is the standard primitive ideal space adorned with a…
For a non-elementary subgroup of the mapping class group of a surface, we study its invariant Radon measures on the space of measured laminations, by classifying them on the recurrent measured laminations. In particular, given a…
For an arbitrary countable directed graph E we show that the only possible values of the stable rank of the associated Cuntz-Krieger algebra C*(E) are 1, 2 or \infty. Explicit criteria for each of these three cases are given. We…
We study diagonal bimodules of \'{e}tale groupoid $C^*$-algebras over their canonical diagonal subalgebras, and establish necessary and sufficient conditions for such a bimodule to be spectral-that is, determined by its spectrum. For a…
We study the braiding statistics of particle-like and loop-like excitations in 2D and 3D gauge theories with finite, Abelian gauge group. The gauge theories that we consider are obtained by gauging the symmetry of gapped, short-range…
We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells), two-band models with any complex couplings and open…
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 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 reduced crossed products of twisted C*-dynamical systems over C*-simple groups. We prove there is a bijective correspondence between maximal ideals of the reduced crossed product and maximal invariant ideals of the underlying…
We introduce $C^*$-algebras associated with directed graphs, along with two generalizations of this concept, namely Exel-Pardo $C^*$-algebras associated with a self-similar action of a group on a directed graph, and the $C^*$-algebras…
A cograph is a simple graph that contains no induced path on four vertices. In this paper, we consider $\mathcal{C}$-graphs, which are a specific class of cographs, defined as $$\overline{\overline{\overline{K_{\alpha_{1}}}\cup…
We characterize when there exists a diagonal preserving $*$-isomorphism between two graph $C^*$-algebras in terms of the dynamics of the boundary path spaces. In particular, we refine the notion of "orbit equivalence" between the boundary…
We study a pair of $C^*$-algebras by associating a $*$-homomorphism from $A$ to $B$ allowing an approximate left-inverse to the sequence algebra of $A$ in a manner reminiscent of several tracial approximation properties. We are particularly…