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SIMPLICIAL HOMOLOGY AND HOCHSCHILD COHOMOLOGY OF BANACH SEMILATTICE ALGEBRAS

Published online by Cambridge University Press:  23 August 2006

YEMON CHOI
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.

Keywords

Primary 46M2046J40Secondary 43A20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 48 , Issue 2 , May 2006 , pp. 231 - 245
Copyright
2006 Glasgow Mathematical Journal Trust

Footnotes

Uses Paul Taylor's diagrams.sty macros.