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It is shown that a C*-algebra generated by any faithful covariant representation of a Hilbert bimodule X is canonically isomorphic to the crossed product associated to X provided that Rieffel's induced representation functor X-ind is…

Operator Algebras · Mathematics 2015-01-30 B. K. Kwasniewski

We introduce a new class of C^*-algebras, which is a generalization of both graph algebras and homeomorphism C^*-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the…

Operator Algebras · Mathematics 2007-05-23 Takeshi Katsura

We give a construction of a nuclear $C^\ast$-algebra associated with an amalgamated free product of groups, generalizing Spielberg's construction of a certain Cuntz-Krieger algebra associated with a finitely generated free product of cyclic…

Operator Algebras · Mathematics 2007-05-23 Rui Okayasu

In this paper we study free actions of groups on separated graphs and their \cstar{}algebras, generalizing previous results involving ordinary (directed) graphs. We prove a version of the Gross-Tucker Theorem for separated graphs yielding a…

Operator Algebras · Mathematics 2022-12-21 Pere Ara , Alcides Buss , Ado Dalla Costa

Let $E$ be a finite directed graph with no sources or sinks and write $X_E$ for the graph correspondence. We study the $C^*$-algebra $C^*(E,Z):=\mathcal{T}(X_E,Z)/\mathcal{K}$ where $\mathcal{T}(X_E,Z)$ is the $C^*$-algebra generated by…

Operator Algebras · Mathematics 2021-08-13 Leonid Helmer , Baruch Solel

Every directed graph defines a Hilbert space and a family of weighted shifts that act on the space. We identify a natural notion of periodicity for such shifts and study their C*-algebras. We prove the algebras generated by all shifts of a…

Operator Algebras · Mathematics 2007-05-23 David W. Kribs , Baruch Solel

We introduce twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs and give a comprehensive treatment of their fundamental structural properties. We establish versions of the usual uniqueness theorems and…

Operator Algebras · Mathematics 2014-08-07 Aidan Sims , Benjamin Whitehead , Michael F. Whittaker

In a recent paper, Pardo and the first named author introduced a class of C*-algebras which which are constructed from an action of a group on a graph. This class was shown to include many C*-algebras of interest, including all Kirchberg…

Operator Algebras · Mathematics 2014-06-30 Ruy Exel , Charles Starling

We develop new techniques for the construction and classification of representations of row-finite and locally convex higher-rank graph C*-algebras O. This class includes Cuntz--Krieger algebras associated to row-finite directed graphs. Our…

Operator Algebras · Mathematics 2026-04-20 Arnaud Brothier , Aidan Sims , Dilshan Wijesena

To every $C^*$ correspondence over a $C^*$-algebra one can associate a Cuntz-Pimsner algebra generalizing crossed product constructions, graph $C^*$-algebras, and a host of other classes of operator algebras. Cuntz-Pimsner algebras come…

Operator Algebras · Mathematics 2019-04-05 Alexandru Chirvasitu

Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs…

Operator Algebras · Mathematics 2007-05-23 Elias Katsoulis , David W. Kribs

The usual crossed product construction which associates to the homeomorphism $T$ of the locally compact space $X$ the C$^*$-algebra $C^*(X,T)$ is extended to the case of a partial local homeomorphism $T$. For example, the Cuntz-Krieger…

Operator Algebras · Mathematics 2007-05-23 Jean Renault

We appeal to results from combinatorial random matrix theory to deduce that various random graph $\mathrm{C}^*$-algebras are asymptotically almost surely Kirchberg algebras with trivial $K_1$. This in particular implies that, with high…

Operator Algebras · Mathematics 2025-05-22 Bhishan Jacelon , Igor Khavkine

We define and investigate properties of universal operator algebras of directed graphs. Results include free products decomposition and continuity of the construction with respect to direct limits. Lastly we prove some K-theoretic results…

Operator Algebras · Mathematics 2007-05-23 Benton L. Duncan

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…

Operator Algebras · Mathematics 2010-01-13 Aidan Sims , Samuel B. G. Webster

We say that a nonselfadjoint operator algebra is partly free if it contains a free semigroup algebra. Motivation for such algebras occurs in the setting of what we call free semigroupoid algebras. These are the weak operator topology closed…

Operator Algebras · Mathematics 2007-05-23 David W. Kribs , Stephen C. Power

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…

Operator Algebras · Mathematics 2011-07-12 P. Ara , K. R. Goodearl

Pure infiniteness (in sense of E.Kirchberg and M.R{\o}rdam) is considered for C*-algebras arising from singly generated dynamical systems. In particular, Cuntz-Krieger algebras and their generalizations, i.e., graph-algebras and O_A of an…

Operator Algebras · Mathematics 2007-05-23 Jacob v. B. Hjelmborg

In this paper, we consider pure infiniteness of generalized Cuntz-Krieger algebras associated to labeled spaces $(E,\mathcal{L},\mathcal{E})$. It is shown that a $C^*$-algebra $C^*(E,\mathcal{L},\mathcal{E})$ is purely infinite in the sense…

Operator Algebras · Mathematics 2017-03-07 Ja A Jeong , Eun Ji Kang , Gi Hyun Park

We prove a spectral theorem for bimodules in the context of graph C*-algebras. A bimodule over a suitable abelian algebra is determined by its spectrum (i.e., its groupoid partial order) iff it is generated by the Cuntz-Krieger partial…

Operator Algebras · Mathematics 2007-05-23 Alan Hopenwasser , Jurtin R. Peters , Stephen C. Power