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### Electronic data

• S0017089506003028a

Rights statement: http://journals.cambridge.org/action/displayJournal?jid=GMJ The final, definitive version of this article has been published in the Journal, Glasgow Mathematical Journal, 48 (2), pp 231-245 2006, © 2006 Cambridge University Press.

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## Simplicial homology and Hochschild cohomology of Banach semilattice algebras

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In: Glasgow Mathematical Journal, Vol. 48, No. 2, 05.2006, p. 231-245.

Research output: Contribution to journalJournal articlepeer-review

### Author

Choi, Yemon. / Simplicial homology and Hochschild cohomology of Banach semilattice algebras. In: Glasgow Mathematical Journal. 2006 ; Vol. 48, No. 2. pp. 231-245.

### Bibtex

@article{795b1cbfed91460f9d27e1fb4cd68b13,
title = "Simplicial homology and Hochschild cohomology of Banach semilattice algebras",
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.",
author = "Yemon Choi",
note = "http://journals.cambridge.org/action/displayJournal?jid=GMJ The final, definitive version of this article has been published in the Journal, Glasgow Mathematical Journal, 48 (2), pp 231-245 2006, {\textcopyright} 2006 Cambridge University Press.",
year = "2006",
month = may,
doi = "10.1017/S0017089506003028",
language = "English",
volume = "48",
pages = "231--245",
journal = "Glasgow Mathematical Journal",
issn = "0017-0895",
publisher = "Cambridge University Press",
number = "2",

}

### RIS

TY - JOUR

T1 - Simplicial homology and Hochschild cohomology of Banach semilattice algebras

AU - Choi, Yemon

N1 - http://journals.cambridge.org/action/displayJournal?jid=GMJ The final, definitive version of this article has been published in the Journal, Glasgow Mathematical Journal, 48 (2), pp 231-245 2006, © 2006 Cambridge University Press.

PY - 2006/5

Y1 - 2006/5

N2 - 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.

AB - 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.

U2 - 10.1017/S0017089506003028

DO - 10.1017/S0017089506003028

M3 - Journal article

VL - 48

SP - 231

EP - 245

JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

SN - 0017-0895

IS - 2

ER -