In this paper, we introduce a weak form of amenability on topological semigroups that call $$\varphi $$ -amenability, where is character semigroup. Some basic properties new notion are obtained and by giving some examples, show definition weaker than the semigroups. As noticeable result, for semigroup S, it shown if S -amenable, then amenable. Moreover, -ergodicity introduced proved under condi...

let s be a semigroup. in certain cases we give some characterizations of extreme amenability of s and we show that in these cases extreme left amenability and extreme right amenability of s are equivalent. also when s is a compact topological semigroup, we characterize extremely left amenable subalgebras of c(s), where c(s) is the space of all continuous bounded real valued functions on s

Let $S$ be an inverse semigroup and let $E$ be its subsemigroup of idempotents. In this paper we define the $n$-th module cohomology group of Banach algebras and show that the first module cohomology group $HH^1_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is zero, for every odd $ninmathbb{N}$. Next, for a Clifford semigroup $S$ we show that $HH^2_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is a Banach sp...

A large class of noncommutative spherical manifolds was obtained recently from cohomology considerations. A one-parameter family of twisted 3-spheres was discovered by Connes and Landi, and later generalized to a three-parameter family by Connes and Dubois-Violette. The spheres of Connes and Landi were shown to be homogeneous spaces for certain compact quantum groups. Here we investigate whethe...

Abstract We give a combinatorial characterization of amenability monomial algebras and prove the existence Følner sequences, answering question due to Ceccherini–Silberstein Samet–Vaillant. then use our that over projectively simple algebras, every module is exhaustively amenable; we conclude convolution minimal subshifts admit same property. deduce any subshift positive entropy gives rise grad...

Our goal in this paper is to define a version of Hochschild homology and cohomology suitable for a class of algebras admitting compatible actions of bialgebras, called “module algebras” (Definition 2.1). Our motivation lies in the following problem: for an algebra A which admits a module structure over an arbitrary bialgebra B compatible with its product structure, the Hochschild or the cyclic ...

We consider the assembly map for principal bundles with fiber a countable discrete group. obtain an index-theoretic interpretation of this homomorphism by providing tensor-product presentation module sections associated to Miščenko line bundle. In addition, we give proof Atiyah’s L2-index theorem in general context flat finitely generated projective Hilbert C∗-modules over compact Hausdorff spa...

One of the key ingredients of A. Connes’ noncommutative geometry is a generalized Dirac operator which induces a metric(Connes’ distance) on the state space. We generalize such a Dirac operator devised by A. Dimakis et al , whose Connes’ distance recovers the linear distance on a 1D lattice, into 2D lattice. This Dirac operator being “naturally” defined has the “local eigenvalue property” and i...