相关论文: Dynamical systems associated with crossed products

We introduce crossed products of a $C^*$-algebra $A$ by a completely positive map $\varrho:A\to A$ relative to an ideal in $A$. They generalize various crossed products by endomorphisms when $\varrho$ is multiplicative. When $A$ is…

A tiling with infinite rotational symmetry, such as the Conway-Radin Pinwheel Tiling, gives rise to a topological dynamical system to which an \'etale equivalence relation is associated. A groupoid C*-algebra for a tiling is produced and a…

We develop the notion of independent resolutions for crossed products attached to totally disconnected dynamical systems. If such a crossed product admits an independent resolution of finite length, then its K-theory can be computed (at…

We introduce a method to study C*-algebras possessing an action of the circle group, from the point of view of its internal structure and its K-theory. Under relatively mild conditions our structure Theorem shows that any C*-algebra, where…

We show that the $\ell^p$-pseudofunctions, which were recently shown to lead to exotic completions of group $C^*$-algebras by Wiersma and the second named author, can be used to construct well-behaved crossed product functors in the sense…

Let $(A,\mathbb{N}^{2},\alpha)$ be a dynamical system consisting of a $C^*$-algebra $A$ and an action $\alpha$ of $\mathbb{N}^{2}$ on $A$ by automorphisms. Let $A\times_{\alpha}^{\textrm{piso}}\mathbb{N}^{2}$ be the partial-isometric…

We study conditions that will ensure that a crossed product of a C*-algebra by a discrete exact group is purely infinite (simple or non-simple). We are particularly interested in the case of a discrete non-amenable exact group acting on a…

We introduce the tracial quasi-Rokhlin property for an automorphism alpha of a unital C*-algebra A, which is not assumed to be simple. We show that under suitable hypotheses, the associated crossed product C*-algebra C*(Z,A,alpha) is…

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…

We show that every topological k-graph constructed from a locally compact Hausdorff space {\Omega} and a family of pairwise commuting local homeomorphisms on {\Omega} satisfying a uniform boundedness condition on the cardinalities of…

Let (A,H,D) be a spectral triple, namely: A is a C*-algebra, H is a Hilbert space on which A acts and D is a selfadjoint operator with compact resolvent such that the set of elements of A having a bounded commutator with D is dense. A…

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…

Given a partial action \alpha of a group G on an associative algebra A we consider the crossed product A x_\alpha G. Using the algebras of multipliers of ideals of A we prove that A x_\alpha G is associative, provided that all ideals of A…

Let $P$ be a unital subsemigroup of a group $G$. We propose an approach to $\mathrm{C}^*$-algebras associated to product systems over $P$. We call the $\mathrm{C}^*$-algebra of a given product system $\mathcal{E}$ its covariance algebra and…

Given a cocycle on a topological quiver by a locally compact group, the author constructs a skew product topological quiver, and determines conditions under which a topological quiver can be identified as a skew product. We investigate the…

There is a connection between the Weyl pseudodifferential calculus and crossed product C*-algebras associated with certain dynamical systems. And in fact both topics are involved in the quantization of a non-relativistic particle moving in…

In order to simultaneously generalize matrix rings and group graded crossed products, we introduce category crossed products. For such algebras we describe the center and the commutant of the coefficient ring. We also investigate the…

We show that when a co-involutive Hopf C*-algebra $S$ coacts via $\delta$ on a C*-algebra $A$, there exists a full crossed product $A\times_\delta S$, with universal properties analogous to those of full crossed products by locally compact…

We prove that a crossed product algebra arising from a minimal dynamical system on the product of the Cantor set and the circle has real rank zero if and only if that system is rigid. In the case that cocycles take values in the rotation…

Partial actions of discrete groups on $C^*$-algebras and the associated crossed products have been studied by Exel and McClanahan. We characterise these crossed products in terms of the spectral subspaces of the dual coaction, generalising…