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SIMPLICIAL HOMOLOGY AND HOCHSCHILD COHOMOLOGY OF BANACH SEMILATTICE ALGEBRAS

Published online by Cambridge University Press:  23 August 2006

YEMON CHOI
Affiliation:
School of Mathematics and Statistics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, England e-mail: y.choi.97@cantab.net
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Abstract

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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.

Type
Research Article
Copyright
2006 Glasgow Mathematical Journal Trust

Footnotes

Uses Paul Taylor's diagrams.sty macros.