Related papers: The ideal structure of reduced crossed products

I combine recent results in the structure theory of nuclear C*-algebras and in topological dynamics to classify certain types of crossed products in terms of their Elliott invariants. In particular, transformation group C*-algebras…

Given a pseudo-free self-similar action of a countable group $G$ on a countable directed graph $E$ with amenable stabilizers of the vertices, we identify the exact conditions under which these stabilizers do not contribute to the ideal…

We consider the intersection $\mathfrak{M}(A)$ of all maximal ideals of an evolution algebra $A$ and study the structure of the quotient $A/\M(A)$. In a previous work, maximal ideals have been related to hereditary subsets of a graph…

A $C^{*}$-algebra $A$ has ideal property if any ideal $I$ of $A$ is generated as a closed two sided ideal by the projections inside the ideal. Suppose that the limit $C^{*}$-algebra $A$ of inductive limit of direct sums of matrix algebras…

Given a separable, AF-algebra A and an inductive limit action on A of a finitely generated abelian group with finite Rokhlin dimension with commuting towers, we give a local description of the associated crossed product C*-algebra. In…

We investigate the higher divisorial ideal $D(I):= Ann(Ext^g_R(R/I,R))$ associated to an ideal I of grade g. Our main focus is the containment problem $D(I) \subseteq \overline{I}$. We show that this inclusion holds for broad classes of…

The basic notion of the article is a pair (A,U), where A is a commutative C*-algebra and U is a partial isometry such that mapping U()U* is an endomorphism of A and U*U belongs to A. We give a description of the maximal ideal space of the…

We show that for a C*-algebra A and a discrete group G with an action of G on A, the reduced crossed product C*-algebra possesses a natural generalization of the convolution product, which we suggest should be named the Hadamard product. We…

Let X be a projective variety, $\sigma$ an automorphism of X, L a $\sigma$-ample invertible sheaf on X, and Z a closed subscheme of X. Inside the twisted homogeneous coordinate ring $B = B(X, L, \sigma)$, let I be the right ideal of…

In the reduced free product of C*-algebras (A,phi)=(A_1,phi_1)*(A_2,phi_2), A is shown to be purely infinite and simple under the hypothesis that A_1 is the crossed product of a C*-algebra by a discrete infinite group, phi_1 is well behaved…

This paper is concerned with the prime spectrum of a tensor product of algebras over a field. It seeks necessary and sufficient conditions for such a tensor product to have the S-property, strong S-property, and catenarity. Its main results…

Following up on previous work, we prove a number of results for C*-algebras with the weak ideal property or topological dimension zero, and some results for C*-algebras with related properties. Some of the more important results include:…

Let $R=k[x,y,z]$ be a standard graded $3$-variable polynomial ring, where $k$ denotes any field. We study grade $3$ homogeneous ideals $I \subseteq R$ defining compressed rings with socle $k(-s)^{\ell} \oplus k(-2s+1)$, where $s \geq3$ and…

Partial dynamical systems (X,alpha) arise naturally when dealing with commutative C*-dynamical system (A,delta). We associate with every pair (X,alpha), or (A,delta), a covariance C*-algebra C*(X,alpha)=C*(A,delta) which agrees with a…

We introduce the concept of Rokhlin dimension for actions of residually compact groups on C*-algebras, which extends and unifies previous notions for actions of compact groups, residually finite groups and the reals. We then demonstrate…

We define and examine sequentially split $*$-homomorphisms between $\mathrm{C}^*$-algebras and $\mathrm{C}^*$-dynamical systems. For a $*$-homomorphism, the property of being sequentially split can be regarded as an approximate weakening of…

We take a new look at dilation theory for nonself-adjoint operator algebras. Among the extremal (co)extensions of a representation, there is a special property of being fully extremal. This allows a refinement of some of the classical…

Let $\alpha : \Gamma \curvearrowright A$ be an action of a discrete group $\Gamma$ on a unital C*-algebra $A$ by *-automorphisms and let $A \rtimes_{\alpha,\lambda} \Gamma$ denote the corresponding reduced crossed product C*-algebra.…

We describe some of the forms of freeness of group actions on noncommutative C*-algebras that have been used, with emphasis on actions of finite groups. We give some indications of their strengths, weaknesses, applications, and…

Building on recent work of Robertson and Steger, we associate a C*-algebra to a combinatorial object which may be thought of as a higher rank graph. This C*-algebra is shown to be isomorphic to that of the associated path groupoid.…