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Simplicial cohomology of band semigroup algebras

Lookup NU author(s): Yemon Choi, Dr Frederic Gourdeau, Dr Michael White

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Abstract

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.


Publication metadata

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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