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The Quarterly Journal of Mathematics Advance Access published online on October 29, 2008
The Quarterly Journal of Mathematics, doi:10.1093/qmath/han027
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© 2008. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

HOCHSCHILD HOMOLOGY AND COHOMOLOGY OF {ell}1(ZFormula)

Yemon Choi{dagger} {ddagger}

Department of Mathematics, Machray Hall, University of Manitoba, Winnipeg, MB, Canada, R3T 2N2

{dagger} E-mail: y.choi.97{at}cantab.net

Received 23 May 2008; revised 3 September 2008
  Abstract

Building on the recent determination of the simplicial cohomology groups of the convolution algebra {ell}1(ZFormula) [F. Gourdeau, Z. A. Lykova and M. C. White, A Künneth formula in topological homology and its applications to the simplicial cohomology of {ell}1(ZFormula), Studia Math. 166 (2005), 29–54], we investigate what can be said for the cohomology of this algebra with more general symmetric coefficients. Our approach leads us to a discussion of the Harrison homology and cohomology in the context of Banach algebras and a development of some of its basic features. As an application of our techniques, we reprove some known results on second-degree cohomology.

{ddagger} Current address: Département de mathématiques, et de statistique, Pavillon Alexandre-Vachon, Université Laval, Québec, QB, Canada, G1V 0A6


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