Cohomology over Banach crossed products. Application to bounded derivations and crossed homomorphisms

Duality Theorems for Crossed Products over Rings

In this note we extend duality theorems for crossed products obtained by M. Koppinen and C. Chen from the case of a base field or a Dedekind domain to the case of an arbitrary noetherian commutative ground ring under fairly weak conditions. In particular we extend an improved version of the celebrated Blattner-Montgomery duality theorem to the case of arbitrary noetherian ground rings.

Crossed complexes, free crossed resolutions and graph products of groups

The category of crossed complexes gives an algebraic model of CW -complexes and cellular maps. Free crossed resolutions of groups contain information on a presentation of the group as well as higher homological information. We relate this to the problem of calculating non-abelian extensions. We show how the strong properties of this category allow for the computation of free crossed resolutions...

The Completely Bounded Approximation Property for Discrete Crossed Products

We consider the relationship between the Haagerup constants for a C-algebra and its crossed product by an amenable group. We prove equality when the group is discrete, and deduce equality when the group is compact and abelian.

The Crossed Menagerie: an introduction to crossed gadgetry and cohomology in algebra

Skew Products and Crossed Products by Coactions

Given a labeling c of the edges of a directed graph E by elements of a discrete group G, one can form a skew-product graph E ×c G. We show, using the universal properties of the various constructions involved, that there is a coaction δ of G on C∗(E) such that C∗(E ×c G) is isomorphic to the crossed product C ∗(E) ×δ G. This isomorphism is equivariant for the dual action δ̂ and a natural action ...