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Simplicial cohomology of band semigroup algebras

Published online by Cambridge University Press:  10 August 2012

Yemon Choi ,
Frédéric Gourdeau  and
Michael C. White
Yemon Choi
Affiliation:
Département de Mathématiques et de Statistique, Pavillon Alexandre-Vachon, Université Laval, Québec (QC) G1V 0A6, Canada ([email protected]; [email protected])
Frédéric Gourdeau
Affiliation:
Département de Mathématiques et de Statistique, Pavillon Alexandre-Vachon, Université Laval, Québec (QC) G1V 0A6, Canada ([email protected]; [email protected])
Michael C. White
Affiliation:
School of Mathematics and Statistics, Herschel Building, Newcastle University, Newcastle-upon-Tyne NE1 7RU, UK ([email protected])
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Abstract

We establish the simplicial triviality of the convolution algebra l1 (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(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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 4 , August 2012 , pp. 715 - 744
Copyright
Copyright © Royal Society of Edinburgh 2012

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