相关论文: Higher rank graph C*-algebras

Every separable nondegenerate C*-correspondence over a commutative C*-algebra with discrete spectrum is isomorphic to a graph correspondence.

Finiteness conditions for $C^*$-algebras like AF-embeddability, quasidiagonality, stable finiteness have been studied by many authors and shown to be equivalent for certain classes of $C^*$-algebras. For example, Schfhauser proves that…

We study the C*-algebra crossed-product of the closed unit disk by the action of one of its conformal automorphisms. After classifying the conformal automorphisms up to topological conjugacy, we investigate, for each class, the irreducible…

We determine the primitive ideal space and hence the ideal lattice of a large class of separable groupoid C*-algebras that includes all 2-graph C*-algebras. A key ingredient is the notion of harmonious families of bisections in etale…

The C*-algebra of a skew-product topological graph is a crossed product of the C*-algebra of the base topological graph by a coaction.

In this paper we generalize the notion of a $k$-graph into (countable) infinite rank. We then define our $C^*$-algebra in a similar way as in $k$-graph $C^*$-algebras. With this construction we are able to find analogues to the Gauge…

We give a new very concrete description of the C*-envelope of the tensor algebra associated to multivariable dynamical system. In the surjective case, this C*-envelope is described as a crossed product by an endomorphism, and as a groupoid…

We investigate the ideal structures of the C^*-algebras arising from topological graphs. We give the complete description of ideals of such C^*-algebras which are invariant under the so-called gauge action, and give the condition on…

We prove that the class of crossed product C*-algebras associated with the action of the multiplicative group of a number field on its ring of finite adeles is rigid in the following explicit sense: Given any *-isomorphism between two such…

I show how to associate a Clifford algebra to a graph. I describe the structure of these Clifford graph algebras and provide many examples and pictures. I describe which graphs correspond to isomorphic Clifford algebras and also discuss…

We present a new method of analysis of associative algebras. This method bears a certain resemblance to the famous analysis of commutative $C^*$-algebras in which an important role is played by multiplicative functionals over the algebra.…

We formalize eight different notions of isomorphism among (unital) graph C*-algebras, and initiate the study of which of these notions may be described geometrically as generated by moves. We propose a list of seven types of moves that we…

The graph C*-algebra of a directed graph E is the universal C*-algebra generated by a family of partial isometries satisfying relations which reflect the path structure of E. In the first part of this paper we consider coverings of directed…

We study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. We develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint…

We consider a free action of an Ore semigroup on a higher-rank graph, and the induced action by endomorphisms of the $C^*$-algebra of the graph. We show that the crossed product by this action is stably isomorphic to the $C^*$-algebra of a…

We prove that every AF-algebra is isomorphic to a crossed product of a commutative AF-algebra by a partial automorphism. The case of UHF-algebras is treated in detail.

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…

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 define centrally large subalgebras of simple unital C*-algebras, strengthening the definition of large subalgebras in previous work. We prove that if A is any infinite dimensional simple separable unital C*-algebra which contains a…

We give a definition of hypergraph C*-algebras. These generalize the well-known graph C*-algebras as well as ultragraph C*-algebras. In contrast to those objects, hypergraph C*-algebras are not always nuclear. We provide a number of…