Related papers: Twisted relative Cuntz-Krieger algebras associated…
For special universal $C^*$-algebras associated to $k$-semigraphs we present the universal representations of these algebras, prove a Cuntz--Krieger uniqueness theorem, and compute the $K$-theory. These $C^*$-algebras seem to be the most…
We show that untwisted respectively twisted conjugacy classes of a compact and simply connected Lie group which satisfy a certain integrality condition correspond naturally to irreducible highest weight representations of the corresponding…
We give a simple and complete picture on the classification of relative Cuntz--Pimsner algebras (and so also of gauge-equivariant representations) using their intuitive parametrisation by kernel--covariance pairs.
The note presents a further study of the class of Cuntz--Krieger type algebras. A necessary and sufficient condition is identified that ensures that the algebra is purely infinite, the ideal structure is studied, % and applied to semigraph…
We introduce higher-rank analogues of the Leavitt path algebras, which we call the Kumjian-Pask algebras. We prove graded and Cuntz-Krieger uniqueness theorems for these algebras, and analyze their ideal structure.
We prove directly that if E is a directed graph in which every cycle has an entrance, then there exists a C*-algebra which is co-universal for Toeplitz-Cuntz-Krieger E-families. In particular, our proof does not invoke ideal-structure…
Given two correspondences X and Y, we show that (under mild hypotheses) the Cuntz-Pimsner algebra of the tensor product of X and Y embeds as a certain subalgebra of the tensor product of the Cuntz-Pimsner algebra of X and the Cuntz=Pimsner…
This paper is comprised of two related parts. First we discuss which k-graph algebras have faithful gauge invariant traces, where the gauge action of $\T^k$ is the canonical one. We give a sufficient condition for the existence of such a…
In this paper, we study a family of $C^*$-subalgebras defined by fixed points of generalized gauge actions of a Cuntz-Krieger algebra, by introducing a family of \'etale groupoids whose associated $C^*$-algebras are these $C^*$-subalgebras.…
We show that $E$ is a finite graph with no sinks if and only if the Leavitt path algebra $L_R(E)$ is isomorphic to an algebraic Cuntz-Krieger algebra if and only if the $C^*$-algebra $C^*(E)$ is unital and…
We introduce the Exel-Pardo $*$-algebra $\mathrm{EP}_R(G,\Lambda)$ associated to a self-similar $k$-graph $(G,\Lambda,\varphi)$. We prove the $\mathbb{Z}^k$-graded and Cuntz-Krieger uniqueness theorems for such algebras and investigate…
We show how the fine structure in shift-tail equivalence, appearing in the noncommutative geometry of Cuntz-Krieger algebras developed by the first two authors, has an analogue in a wide range of other Cuntz-Pimsner algebras. To illustrate…
A twisting system is one of the major tools to study graded algebras, however, it is often difficult to construct a (non-algebraic) twisting system if a graded algebra is given by generators and relations. In this paper, we show that a…
A general method of investigation of the uniqueness property for $C^*$-algebra equipped with a circle gauge action is discussed. It unifies isomorphism theorems for various crossed products and Cuntz-Krieger uniqueness theorem for…
We produce a complete descrption of the lattice of gauge-invariant ideals in $C^*(\Lambda)$ for a finitely aligned $k$-graph $\Lambda$. We provide a condition on $\Lambda$ under which every ideal is gauge-invariant. We give conditions on…
We construct a covariant functor from the topological torus bundles to the so-called Cuntz-Krieger algebras; the functor maps homeomorphic bundles into the stably isomorphic Cuntz-Krieger algebras. It is shown, that the K-theory of the…
We investigate $C^*$-algebras associated with row-finite topological higher-rank graphs with no source, which are based on product system $C^*$-algebras. We prove the Cuntz-Krieger uniqueness theorem, and provide the condition of simplicity…
We use product systems of $C^*$-correspondences to introduce twisted $C^*$-algebras of topological higher-rank graphs. We define the notion of a continuous $\mathbb{T}$-valued $2$-cocycle on a topological higher-rank graph, and present…
To an arbitrary directed graph we associate a row-finite directed graph whose C*-algebra contains the C*-algebra of the original graph as a full corner. This allows us to generalize results for C*-algebras of row-finite graphs to…
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…