Newcastle University

publication:

The cyclic and simplicial cohomology of the bicyclic semigroup algebra (2011)

Author(s): Gourdeau F, White MC

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).

• Date: 26-04-2010
• Journal: Quarterly Journal of Mathematics
• Volume: 62
• Issue: 3
• Pages: 607-624
• Publisher: Oxford University Press
• Publication type: Article
• Bibliographic status: Published

• URL: http://dx.doi.org/10.1093/qmath/haq014
• DOI: 10.1093/qmath/haq014
• ISSN (electronic): 1464-3847

Staff

Dr Michael White Senior Lecturer

Email: michael.white@ncl.ac.uk Telephone: +44 (0) 191 222 7304