In this paper we construct a cylindrical module A♮H for an Hcomodule algebra A, where the antipode of the Hopf algebra H is bijective. We show that the cyclic module associated to the diagonal of A♮H is isomorphic with the cyclic module of the crossed product algebra A ⋊H. This enables us to derive a spectral sequence for the cyclic homology of the crossed product algebra. We also construct a c...

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 group, it is also shown that rigidity implies tracial rank zero, and in particular, the crossed product algebra is isomorphic to a unital simple AT-algebra of ...

Starting from a discrete C⁎-dynamical system (A,θ,ωo), we define and study most of the main ergodic properties crossed product (A⋊αZ,Φθ,u,ωo∘E), E:A⋊αZ→A being canonical conditional expectation A⋊αZ onto A, provided α∈Aut(A) commute with ⁎-automorphism θ up to unitary u∈A. Here, Φθ,u∈Aut(A⋊αZ) can be considered as fully noncommutative generalisation celebrated skew-product defined by H. Anzai f...

The paper presents a construction of the crossed product of a C-algebra by a commutative semigroup of bounded positive linear maps generated by partial isometries. In particular, it generalizes Antonevich, Bakhtin, Lebedev’s crossed product by an endomorphism, and is related to Exel’s interactions. One of the main goals is the Isomorphism Theorem established in the case of actions by endomorphi...

An action of Z by automorphisms of a k-graph induces an action of Z by automorphisms of the corresponding k-graph C∗-algebra. We show how to construct a (k + l)-graph whose C∗-algebra coincides with the crossed product of the original k-graph C∗-algebra by Z. We then investigate the structure of the crossed-product C∗-algebra.

An action of Z by automorphisms of a k-graph induces an action of Z by automorphisms of the corresponding k-graph C∗-algebra. We show how to construct a (k + l)-graph whose C∗-algebra coincides with the crossed product of the original k-graph algebra by Z. We then investigate the structure of the crossed-product C∗-algebra.

For an infinitesimal symplectic action of a Lie algebra g on a symplectic manifold, we construct an infinitesimal crossed product of Hamiltonian vector fields and Lie algebra g. We obtain its second crossed product in case g = R and show an infinitesimal version for a theorem type of Takesaki duality.

For an infinitesimal symplectic action of a Lie algebra g on a symplectic manifold, we construct an infinitesimal crossed product of Hamiltonian vector fields and Lie algebra g. We obtain its second crossed product in case g = R and show an infinitesimal version for a theorem type of Takesaki duality.