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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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