Let $L$ be a finite Galois field extension of $K$ with group $G$. We decompose any idempotent 2-cocycle $f$ using sequences descending two-sided ideals the corresponding weak crossed product algebra $A_f$. specialize results in

If $ \alpha is an action of a locally compact group G on dual operator space $ X $, then two generally different notions crossed products are defined, namely the Fubini product X\mathbin {\rtimes^{\mathcal {F}} _{\alpha }}

In this paper we prove that the noncyclic generic abelian crossed product p-algebras constructed by Amitsur and Saltman in [AS78] remain noncyclic after tensoring by any prime to p extension of their centers. We also prove that an example due to Saltman of an indecomposable generic abelian crossed product with exponent p and degree p 2 remains indecomposable after any prime to p extension. 0 In...

The C∗-algebra C∗(E) of a directed graph E is generated by partial isometries satisfying relations which reflect the path structure of the graph. In [10], Kumjian and Pask considered the action of a group G on C∗(E) induced by an action of G on E. They proved that if G acts freely and E is locally finite, then the crossed product C∗(E) × G is Morita equivalent to the C∗-algebra of the quotient ...

Many important C∗-algebras, such as AF-algebras, Cuntz-Krieger algebras, graph algebras and foliation C∗-algebras, are the C∗-algebras of r-discrete groupoids. These C∗-algebras are often associated with inverse semigroups through the C∗-algebra of the inverse semigroup [HR90] or through a crossed product construction as in Kumjian’s localization [Kum84]. Nica [Nic94] connects groupoid C∗-algeb...

In this work we define two kinds of crested product for reversible Markov chains, which naturally appear as a generalization of the case of crossed and nested product, as in association schemes theory, even if we do a construction that seems to be more general and simple. Although the crossed and nested product are inspired by the study of Gelfand pairs associated with the direct and the wreath...

Let A be a Hopf algebra in a braided category C. Crossed modules over A are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category DY (C)AA of crossed modules is braided and is a concrete realization of a known general construction of a double or center of a monoidal category. For a quantum braided group (A,A,R) the correspo...

Several versions of approximate conjugacy for minimal dynamical systems are introduced. Relation between approximate conjugacy and corresponding crossed product C∗-algebras is discussed. For the Cantor minimal systems, a complete description is given for these relations via K-theory and C∗-algebras. For example, it is shown that two Cantor minimal systems are approximately τ -conjugate if and o...

We use the canonical Lipschitz geometry available on the boundary of a hyperbolic group to construct finitely summable Fredholm modules over the crossed product of the boundary action. The procedure yields a full set of representatives of the K-homology of the crossed product, and all of them are p-summable for p in an appropriate range related to the geometry of the boundary. By restricting th...

Let A be a unital separable simple C∗-algebra with TR(A) ≤ 1 and α be an automorphism. We show that if α satisfies the tracially cyclic Rokhlin property then TR(A ⋊α Z) ≤ 1. We also show that whenever A has a unique tracial state and αm is uniformly outer for each m and αr is approximately inner for some r > 0, α satisfies the tracial cyclic Rokhlin property. By applying the classification theo...