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Lookup NU author(s): Yemon Choi, Dr Frederic Gourdeau, Dr Michael White
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We establish the simplicial triviality of the convolution algebra l(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 l(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.
Author(s): White MC; Choi Y; Gourdeau F
Publication type: Article
Publication status: Published
Journal: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Year: 2012
Volume: 142
Issue: 4
Pages: 715-744
Print publication date: 10/08/2012
ISSN (print): 0308-2105
ISSN (electronic): 1473-7124
Publisher: The RSE Scotland Foundation
URL: http://dx.doi.org/10.1017/S0308210510000648
DOI: 10.1017/S0308210510000648
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