Simplicial homology and Hochschild cohomology of Banach semilattice algebras

Details Simplicial homology and Hochschild cohomology of Banach semilattice algebras Simplicial homology and Hochschild cohomology of Banach semilattice algebras

2006-06-15

arxiv.org/abs/math/0606364v1

Glasgow Math. Journal 48 (2006), no. 2, 231--245.

Mathematics

Functional Analysis

17pp, preprint version (revised 2006). Final version to appear in Glasgow Math. Journal (2006)

Scientific paper

10.1017/S0017089506003028

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.

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