Related papers: Crossed products of operator systems

In this paper we introduce an analog of the tracial Rokhlin property, called the {\emph {projection free tracial Rokhlin property}}, for $C^*$-algebras which may not have any nontrivial projections. Using this we show that if $A$ is an…

We define and study fibrations of topological groupoids. We interpret a groupoid fibration L->H with fibre G as an action of H on G by groupoid equivalences. Our main result shows that a crossed product for an action of L is isomorphic to…

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…

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…

Given groupoids $G$ and $H$ and a $(G,H)$-equivalence $X$ we may form the transformation groupoid $G\ltimes X\rtimes H$. Given a separable groupoid dynamical system $(A,G\ltimes X\rtimes H,\omega)$ we may restrict $\omega$ to an action of…

Given a local homeomorphism \sigma:U -> X where U is a clopen subset of an compact and Hausdorff topological space X, we obtain the possible transfer operators L_\rho which may occur for \al:C(X) -> C(U) given by \al(f)=f\sigma. We obtain…

Let $(\mathcal{A}, G, \alpha)$ be a groupoid dynamical system. We show that if $G$ is assumed to be measurewise amenable and the section algebra $A = \Gamma_0(G^{(0)}, \mathcal{A})$ is nuclear, then the associated groupoid crossed product…

There are many different crossed products by an endomorphism of a C*-algebra, and constructions by Exel and Stacey have proved particularly useful. Here we show that every Exel crossed product is isomorphic to a Stacey crossed product…

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…

Given a closed ideal I in a C*-algebra A, an ideal J (not necessarily closed) in I, a *-homomorphism \al:A --> M(I) and a map L:J --> A with some properties, based on [3] and [9] we define a C*-algebra O(A,\al,L) which we call the "Crossed…

We study the semicrossed product of a finite dimensional C^*-algebra by two types of commuting automorphisms, and identify them with matrix algebras of analytic functions in two variables. We look at the connections with semicrossed…

We show that if $(X.A)$ and $(Y,B)$ are two isomorphic Hilbert pro-$C^{\ast} $-bimodules, then the crossed product $A\times_{X}\mathbb{Z}$ of $A$ by $X$ and the crossed product $B\times_{Y}\mathbb{Z}$ of $B$ by $Y$ are isomorphic as…

Let $\Gamma^+$ be the positive cone in a totally ordered abelian group $\Gamma$, and let $\alpha$ be an action of $\Gamma^+$ by endomorphisms of a $C^*$-algebra $A$. We consider a new kind of crossed-product $C^*$-algebra…

The cross product frequently occurs in Physics and Engineering, since it has large applications in many contexts, e.g. for calculating angular momenta, torques, rotations, volumes etc. Though this mathematical operator is widely used, it is…

We put two C*-algebras together in a noncommutative tensor product using quantum group coactions on them and a bicharacter relating the two quantum groups that act. We describe this twisted tensor product in two equivalent ways. The first…

We characterize when a C*-cover admits a C*-dynamical extension of dynamics on an operator algebra in terms of the boundary ideal structure for the operator algebra in its maximal representation and show that the C*-covers that admit such…

Given a minimal action $G\curvearrowright X$ of a countable group $G$ on a compact space $X$, we prove that if the reduced crossed product $G\ltimes_rC(X)$ is simple, then there exists a point whose stabilizer subgroup has trivial amenable…

This work is motivated by Radulescu's result on the comparison of C*-tensor norms on C*(F_n) x C*(F_n). For unital C*-algebras A and B, there are natural inclusions of A and B into their unital free product, their maximal tensor product and…

In this article, we consider a twisted partial action $\alpha$ of a group $G$ on a ring $R$ and it is associated partial crossed product $R*_{\alpha}^wG$. We study necessary and sufficient conditions for the commutativity and simplicity of…

We consider reduced crossed products of twisted C*-dynamical systems over C*-simple groups. We prove there is a bijective correspondence between maximal ideals of the reduced crossed product and maximal invariant ideals of the underlying…