A UNIFORM COHOMOLOGY THEORY FOR ALGEBRAS

A Cohomology Theory for Commutative Algebras. Ii1

1. Introduction. In the first paper of this series [l], henceforth referred to as I, we define a cohomology theory for a commutative algebra P with coefficients in an P-module M for which H2(R, M) is the group of singular extensions of P by M. In this paper we generalize to a cohomology 22(5, <b, M) where (S, <p) is a singular extension of P and M is an P-module. The second group is again a gro...

A Cohomology Theory for Commutative Algebras. I1

1. Introduction. D. K. Harrison has recently developed a co-homology theory for commutative algebras over a field [2]. A few key theorems are proved and the results applied to the theory of local rings and eventually to algebraic geometry. The main problem is that both his definitions and proofs require involved calculations. In this paper we define a cohomology theory which (a) relies on more ...

Cyclic theory for commutative differential graded algebras and s–cohomology

In this paper one considers three homotopy functors on the category of manifolds , hH∗, cH∗, sH∗, and parallel them with other three homotopy functors on the category of connected commutative differential graded algebras, HH∗, CH∗, SH∗. If P is a smooth 1-connected manifold and the algebra is the de-Rham algebra of P the two pairs of functors agree but in general do not. The functors HH∗ and CH...

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...

Second Hochschild Cohomology of Convolution Algebras