The cyclic and simplicial cohomology of the Cuntz semigroup algebra
| Autor: | Frédéric Gourdeau, Michael C. White |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
Primary 46H20
43A20 Secondary 16E40 Mathematics::Operator Algebras Group cohomology Applied Mathematics 010102 general mathematics 01 natural sciences h-vector Mathematics::Algebraic Topology Cohomology Algebra Mathematics - Functional Analysis Simplicial complex Mathematics::K-Theory and Homology 0103 physical sciences De Rham cohomology Equivariant cohomology 010307 mathematical physics 0101 mathematics Banach *-algebra Čech cohomology Analysis Mathematics |
| Popis: | The main objective of this paper is to determine the simplicial and cyclic cohomology groups of the Cuntz semigroup algebra $\ell^1(\Cuntz)$. In order to do so, we first establish some general results which can be used when studying simplicial and cyclic cohomology of Banach algebras in general. We then turn our attention to $\ell^1(\Cuntz)$, showing that the cyclic cohomology groups of degree $n$ vanish when $n$ is odd and are one-dimensional when $n$ is even ($n\ge 2$). Using the Connes-Tzygan exact sequence, these results are used to show that the simplicial cohomology groups of degree $n$ vanish for $n\ge 1$. We also determine the simplicial and cyclic cohomology of the tensor algebra of a Banach space, a class which includes the algebra on the free semigroup on $m$-generators $\ell^1(\FS)$. Comment: 18 pages |
| Databáze: | OpenAIRE |
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