Simplicial homology and Hochschild cohomology of Banach semilattice algebras
Abstract
Description
The ${\ell}^1$-convolution algebra of a semilattice is known to have trivial cohom ology in degrees 1,2 and 3 whenever the coefficient bimodule is symmetric. We ex tend this result to all cohomology groups of degree $\geq 1$ with symmetric coef ficients. Our techniques prove a stronger splitting result, namely that the spli tting can be made natural with respect to the underlying semilattice.
17pp, preprint version (revised 2006). Final version to appear in Glasgow Math. Journal (2006)
17pp, preprint version (revised 2006). Final version to appear in Glasgow Math. Journal (2006)