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The cyclic and simplicial cohomology of the Cuntz semigroup algebra

Lookup NU author(s): Dr Frederic Gourdeau, Dr Michael White

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Abstract

The main objective of this paper is to determine the simplicial and cyclic cohomology groups of the Cuntz semigroup algebra l(1) (S-m). 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 l(1) (FSm). 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 l(1) (S-m), showing that the cyclic cohomology groups of degree n vanish when n is odd and are one-dimensional when n is even (n >= 2). Using the Connes-Tzygan exact sequence, these results are used to show that the simplicial cohomology groups of degree n vanish for n >= 1. A similar strategy is used for the tensor algebra of a Banach space. (C) 2011 Elsevier Inc. All rights reserved.

Publication metadata

Author(s): Gourdeau F, White MC

Publication type: Article

Publication status: Published

Journal: Journal of Mathematical Analysis and Applications

Year: 2012

Volume: 386

Issue: 2

Pages: 921-932

Print publication date: 15/02/2012

ISSN (print): 0022-247X

ISSN (electronic): 1096-0813

Publisher: Academic Press

URL: http://dx.doi.org/10.1016/j.jmaa.2011.08.050

DOI: 10.1016/j.jmaa.2011.08.050

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