# Simplicial cohomology of band semigroup algebras

Choi, Yemon and Gourdeau, Frédéric and White, Michael C. (2012) Simplicial cohomology of band semigroup algebras. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 142 (4). pp. 715-744. ISSN 1473-7124

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## Abstract

We establish the simplicial triviality of the convolution algebra $\ell^1(S)$, where $S$ is a band semigroup. This generalizes some results of Choi (Glasgow Math. J. 48 (2006), 231–245; Houston J. Math. 36 (2010), 237–260). To do so, we show that the cyclic cohomology of this algebra vanishes in all odd degrees, and is isomorphic in even degrees to the space of continuous traces on $\ell^1(S)$. Crucial to our approach is the use of the structure semilattice of $S$, and the associated grading of $S$, together with an inductive normalization procedure in cyclic cohomology. The latter technique appears to be new, and its underlying strategy may be applicable to other convolution algebras of interest.

Item Type:
Journal Article
Journal or Publication Title:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
http://journals.cambridge.org/action/displayJournal?jid=PRM The final, definitive version of this article has been published in the Journal, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 142 (4), pp 715-744 2012, © 2012 Cambridge University Press
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
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ID Code:
68294
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Deposited On:
24 Jan 2014 05:51
Refereed?:
Yes
Published?:
Published