Cohomology for Operator Algebras: The Mayer–Vietoris Sequence

Dirac Cohomology for the Cubic Dirac Operator

Let g be a complex semisimple Lie algebra and let r ⊂ g be any reductive Lie subalgebra such that B|r is nonsingular where B is the Killing form of g. Let Z(r) and Z(g) be, respectively, the centers of the enveloping algebras of r and g. Using a Harish-Chandra isomorphism one has a homomorphism η : Z(g) → Z(r) which, by a well-known result of H. Cartan, yields the the relative Lie algebra cohom...

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 the Operator Formalism

This letter points a close parallel between the operator formalism for string theory and the action of a Lie algebra on a differential complex. The construction of conformal field theories can then be regarded as a cohomology problem; we suggest that this viewpoint may survive the generalization beyond finite genus Riemann surfaces. Disciplines Physical Sciences and Mathematics | Physics This j...

Second Hochschild Cohomology of Convolution Algebras

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 ...