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Simplicial cohomology of band semigroup algebras


Yemon Choi*, Frédéric Gourdeau, Michael C. White

* Corresponding author



MSC 2010: Primary 16E40, 43A20


Appeared as Proc. Roy. Soc. Edinburgh Sect. A 142 (2012), no. 4, 715--744.

Copyright is held by the Royal Society of Edinburgh; they have agreed that I can put a PDF of the final published version on my webpages, so here it is.

Preprint version available at arXiv 1004.2301


[ Math Review (summary) | Zentralblatt ]


We establish simplicial triviality of the convolution algebra l1(S), where S is a band semigroup. This generalizes results of the first author (Glasgow Math. Journal, 2006; Houston J. Math, 2010). 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 l1(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.


This work was done while I was a postdoctoral researcher at Université Laval, under Gourdeau's supervision. Some of the work was done during visits to the University of Newcastle upon Tyne, hosted by White.

Yemon Choi