Simplicial homology and Hochschild cohomology of Banach semilattice algebras

Choi, Yemon (2006) Simplicial homology and Hochschild cohomology of Banach semilattice algebras. Glasgow Mathematical Journal, 48 (2). pp. 231-245. ISSN 0017-0895

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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.