THE CYCLIC AND SIMPLICIAL COHOMOLOGY OF THE BICYCLIC SEMIGROUP ALGEBRA

Autor:	Frédéric Gourdeau, Michael C. White
Rok vydání:	2010
Předmět:	Exact sequence Mathematics::Operator Algebras Semigroup General Mathematics Group cohomology Cyclic homology Mathematics::Algebraic Topology Cohomology Algebra Mathematics::K-Theory and Homology Bicyclic semigroup Equivariant cohomology Mathematics Resolution (algebra)
Zdroj:	The Quarterly Journal of Mathematics. 62:607-624
ISSN:	1464-3847 0033-5606
DOI:	10.1093/qmath/haq014
Popis:	Let □ = l 1 (ℬ) be the semigroup algebra of ℬ, the bicyclic semigroup. We give a resolution of l ∞ (ℬ) which simplifies the computation of the cohomology of l 1 (ℬ) dual bimodules. We apply this to the dual module l ∞ (ℬ) and show that the simplicial cohomology groups ℋ n (□, □′) vanish for n ≥ 2. Using the Connes–Tzygan exact sequence, these results are used to show that the cyclic cohomology groups ℋ□ n (□, □′) vanish when n is odd and are one-dimensional when n is even (n ≥ 2).
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c9d96dcb687eda0019a4dc6a1cd7405c https://doi.org/10.1093/qmath/haq014 Zobrazit plný text záznamu