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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Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -