Abstract Let $\phi :X\to X$ be a homeomorphism of compact metric space X . For any continuous function $F:X\to \mathbb {R}$ there is one-parameter group $\alpha ^{F}$ automorphisms (or flow) on the crossed product $C^*$ -algebra $C(X)\rtimes _{\phi }\mathbb {Z}$ defined such that ^{F}_{t}(fU)=fUe^{-itF}$ when $f \in C(X)$ and U canonical unitary in construction product. In this paper we study K...

A holomorphic quadratic differential on a hyperbolic Riemann surface has an associated measured foliation, which can be straightened to yield a measured geodesic lamination. On the other hand, a quadratic differential can be considered as the Schwarzian derivative of a CP1 structure, to which one can naturally associate another measured geodesic lamination (using grafting). We compare these two...

We show that a minimal action of finitely generated group polynomial growth on compact metrizable space has comparison. It follows if such an is free and the small boundary property then it almost finite its C⁎-crossed product Z-stable, consequently crossed products are classified by their Elliott invariant.

For a given Jacobi-Jordan algebra A and vector space V over field k , non-abelian cohomological type object H 2 ( ) is constructed: it classifies all algebras containing as subalgebra of codimension equal to dim . Any such isomorphic so-called unified product ♮ Furthermore, we introduce the bicrossed (semi-direct, crossed, or skew crossed) ⋈ associated two special case product. Several examples...

We show that when a co-involutive Hopf C *-algebra S coacts via δ on a C *-algebra A, there exists a full crossed product A × δ S, with universal properties analogous to those of full crossed products by locally compact groups. The dual Hopf C *-algebra is then defined byˆS := C × id S.