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The cyclic and simplicial cohomology of the bicyclic semigroup algebra

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

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Abstract

Let = 1() be the semigroup algebra of , the bicyclic semigroup. We give a resolution of () which simplifies the computation of the cohomology of 1() dual bimodules. We apply this to the dual module () and show that the simplicial cohomology groups n(, ') vanish for n 2. Using the Connes–Tzygan exact sequence, these results are used to show that the cyclic cohomology groups n(, ') vanish when n is odd and are one-dimensional when n is even (n 2).

Publication metadata

Author(s): Gourdeau F, White MC

Publication type: Article

Publication status: Published

Journal: Quarterly Journal of Mathematics

Year: 2011

Volume: 62

Issue: 3

Pages: 607-624

Print publication date: 26/04/2010

ISSN (print): 0033-5606

ISSN (electronic): 1464-3847

Publisher: Oxford University Press

URL: http://dx.doi.org/10.1093/qmath/haq014

DOI: 10.1093/qmath/haq014

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