Cohomology and Deformation of Module-algebras

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...

MODULE GENERALIZED DERIVATIONS ON TRIANGULAUR BANACH ALGEBRAS

Let $A_1$, $A_2$ be unital Banach algebras and $X$ be an $A_1$-$A_2$- module. Applying the concept of module maps, (inner) modulegeneralized derivations and  generalized first cohomology groups, wepresent several results concerning the relations between modulegeneralized derivations from $A_i$ into the dual space $A^*_i$ (for$i=1,2$) and such derivations  from  the triangular Banach algebraof t...

A comment concerning cohomology and invariants of Lie algebras with respect to contractions and deformations

Contrary to the expected behavior, we show the existence of noninvertible deformations of Lie algebras which can generate invariants for the coadjoint representation, as well as delete cohomology with values in the trivial or adjoint module. A criterion to decide whether a given deformation is invertible or not is given in dependence of the Poincaré polynomial. PACS numbers: 02.20Sv, 02.20Qs, 9...

Projective connections, group Vey cocycle and deformation quantization

0.1. In this paper we construct a number of geometrically meaningful 1– and 2– cocycles of infinite dimensional Lie groups and Lie algebras. The groups are groups of diffeomorphisms of smooth manifolds and their subgroups, such as the group of symplectomorphisms of a symplectic manifold; the Lie algebras are algebras of vector fields. Coefficient spaces of the cocycles are spaces of various ten...

First Order Cohomology of l^1-Munn Algebras and Certain Semigroup Algebras