The cyclic and simplicial cohomology of the bicyclic semigroup algebra

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  2. Dr Frederic Gourdeau
  3. Dr Michael White
Author(s)Gourdeau F, White MC
Publication type Article
JournalQuarterly Journal of Mathematics
ISSN (print)0033-5606
ISSN (electronic)1464-3847
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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).
PublisherOxford University Press
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