Axiomatic cohomology of operator 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...

Second Hochschild Cohomology of Convolution Algebras

Axiomatic Characterization of Ordinary Differential Cohomology

Ĥ satisfies the Character Diagram shown in §1 and thus has natural transformations onto both closed differential forms with integral periods and integral cohomology. It was shown in [6] that an enriched version of the Weil homomorphism, carrying both an invariant polynomial and an associated integral homology class of the classifying space, naturally factors through Ĥ on its way to these target...

Cohomology of Effect Algebras

We will define two ways to assign cohomology groups to effect algebras, which occur in the algebraic study of quantum logic. The first way is based on Connes’ cyclic cohomology. The resulting cohomology groups are related to the state space of the effect algebra, and can be computed using variations on the Künneth and Mayer–Vietoris sequences. The second way involves a chain complex of ordered ...

Cohomology of Hecke Algebras

We compute the cohomology H∗(H, k) = ExtH(k, k) where H = H(n, q) is the Hecke algebra of the symmetric group Sn at a primitive `th root of unity q, and k is a field of characteristic zero. The answer is particularly interesting when ` = 2, which is the only case where it is not graded commutative. We also carry out the corresponding computation for Hecke algebras of type Bn and Dn when ` is odd.