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Simplicial homology and Hochschild cohomology of Banach semilattice algebras

Authors

Yemon Choi

Keywords

semilattices, Hochschild cohomology, Banach algebras

Status

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

Preprint version available at arXiv math.FA/0606364

Reviews

[ Math Reviews | Zentralblatt ]

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.

Updates/comments

In one of the passing remarks, a background result in semigroup theory is misquoted (this does not affect the results of the paper). For more details see the list of corrections.

The paper of Gourdeau--Pourabbas--White, referred to in the references as a preprint, has appeared as

F. Gourdeau, A. Pourabbas, M. C. White, Simplical cohomology of some semigroup algebras, Canad. Math. Bull. 50 (2007), no. 1, 56--70. [ Math Reviews | Zbl ]


Yemon Choi
Last modified: Mon Mar 1 12:17:02 EDT 2010