SIMPLICIAL HOMOLOGY AND HOCHSCHILD COHOMOLOGY OF BANACH SEMILATTICE ALGEBRAS
Published online by Cambridge University Press: 23 August 2006
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.
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- Research Article
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- 2006 Glasgow Mathematical Journal Trust
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