Group pairs with periodic cohomology

On the Cohomology of Weakly Almost Periodic Group Representations

We initiate a study of cohomological aspects of weakly almost periodic group representations on Banach spaces, in particular, isometric representations on reflexive Banach spaces. Using the Ryll-Nardzewski fixed point Theorem, we prove a vanishing result for the restriction map (with respect to a subgroup) in the reduced cohomology of weakly periodic representations. Combined with the Alaoglu-B...

Module cohomology group of inverse semigroup algebras

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...

Cohomology and Deformation of Leibniz Pairs

Cohomology and deformation theories are developed for Poisson algebras starting with the more general concept of a Leibniz pair, namely of an associative algebra A together with a Lie algebra L mapped into the derivations of A. A bicomplex (with both Hochschild and Chevalley-Eilenberg cohomologies) is essential. The importance of Poisson algebras in classical mechanics makes it useful to have a...

Motivic Cohomology of Pairs of Simplices

Let F be a eld and n> 2 be a positive integer. A simplex in the projective space P F is an ordered set of hyperplanes L 1⁄4 ðL0; . . . ; LnÞ. A face of L is any nonempty intersection of the hyperplanes. A pair of simplices is admissible if they do not have common faces of the same dimension. It is a generic pair if all the faces of the two simplices are in general position. In their seminal pap...

The Cohomology of a Coxeter Group with Group Ring Coefficients