相关论文: Invariance of the Cuntz splice

We geometrically describe the relation induced on a set of graphs by isomorphism of their associated graph C*-algebras as the smallest equivalence relation generated by five types of moves. The graphs studied have finitely many vertices and…

We give a notion of quantum automorphism group of graph C*-algebras without sink at critical inverse temperature. This is defined to be the universal object of a category of CQG's having a linear action in the sense of [11] and preserving…

Let $\xi:C^*(E)\to C^*(F)$ be a unital $*$-homomorphism between simple purely infinite Cuntz-Krieger algebras of finite graphs. We prove that there exists a unital $*$-homomorphism $\phi:L(E)\to L(F)$ between the corresponding Leavitt…

The structure of the $C^*$-algebras corresponding to even-dimensional mirror quantum spheres is investigated. It is shown that they are isomorphic to both Cuntz-Pimsner algebras of certain $C^*$-correspondences and $C^*$-algebras of certain…

We introduce regular closed subgraphs of Katsura's topological graphs and use them to generalize the notion of an adjunction space from topology. Our construction attaches a topological graph onto another via a regular factor map. We prove…

The problem of inner vs outer conjugacy of subalgebras of certain graph C*-algebras is investigated. For a large class of finite graphs E, we show that whenever $\alpha$ is a vertex-fixing quasi-free automorphism of the corresponding graph…

Let E be a row-finite directed graph. We prove that there exists a C*-algebra C*_{min}(E) with the following co-universal property: given any C*-algebra B generated by a Toeplitz-Cuntz-Krieger E-family in which all the vertex projections…

We prove that an isomorphism of graded Grothendieck groups $K^{gr}_0$ of two Leavitt path algebras induces an isomorphism of a certain quotient of algebraic filtered $K$-theory and consequently an isomorphism of filtered $K$-theory of their…

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…

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…

Suppose that A is a C*-algebra for which A is isomorphic to A tensor Z, where Z is the Jiang-Su algebra: a unital, simple, stably finite, separable, nuclear, infinite dimensional C*-algebra with the same Elliott invariant as the complex…

The Calkin algebra is not isomorphic to the corona of the stabilization of the Cuntz algebra~${\mathcal O}_\infty$, any other Kirchberg algebra, or even the corona of the stabilization of any unital, ${\mathcal Z}$-stable ${\mathrm…

In this paper we show that the universal C*-algebra satisfying the Cuntz-Li relations is generated by an inverse semigroup of partial isometries. We apply Exel's theory of tight representations to this inverse semigroup. We identify the…

Let A be a simple, unital, exact, and finite C*-algebra which absorbs the Jiang-Su algebra Z tensorially. We prove that the Cuntz semigroup of A admits a complete order embedding into an ordered semigroup obtained from the Elliott invariant…

We show that for a sofic shift Lambda, Matsumoto's C*-algebra O_Lambda is isomorphic to the Cuntz-Krieger algebra of the left Krieger cover graph of Lambda.

Given an arbitrary countable directed graph $G$ we prove the C*-envelope of the tensor algebra $T_+(G)$ coincides with the universal Cuntz-Krieger algebra associated with $G$. Our approach is concrete in nature and does not rely on Hilbert…

In this paper we analyze the structure of C*-algebras associated to ultragraphs, which are generalizations of directed graphs. We characterize the simple ultragraph algebras as well as deduce necessary and sufficient conditions for an…

We investigate Cuntz-Pimsner $C^*$-algebras associated with certain correspondences of the unit circle $\mathbb{T}$. We analyze these $C^*$-algebras by analogy with irrational rotation algebras $A_\theta$ and Cuntz algebras $\mathcal{O}_n$.…

We study permanence properties of the classes of stable and so-called D-stable C*-algebras, respectively. More precisely, we show that a C_0(X)-algebra A is stable if all its fibres are, provided that the underlying compact metrizable space…

I introduce yet another way to associate a C*-algebra to a graph and construct a simple nuclear C*-algebra that has irreducible representations both on a separable and a nonseparable Hilbert space.