## Simplicial homology and Hochschild cohomology of Banach semilattice algebras

Yemon Choi

#### Keywords

semilattices, Hochschild cohomology, Banach algebras

#### Status

Preprint version available at arXiv math.FA/0606364

#### Abstract

The ${\ell}^1$-convolution algebra of a semilattice is known to have trivial cohomology in degrees 1,2 and 3 whenever the coefficient bimodule is symmetric. We extend this result to all cohomology groups of degree $\geq 1$ with symmetric coefficients. Our techniques prove a stronger splitting result, namely that the splitting can be made natural with respect to the underlying semilattice.