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Simplicial homology and Hochschild cohomology of Banach semilattice algebras

Yemon Choi
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Abstract

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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Yemon Choi. 2006-06-15. Simplicial homology and Hochschild cohomology of Banach semilattice algebras. https://doi.org/10.1017/s0017089506003028

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