Lookup NU author(s): Dr Frederic Gourdeau,
Dr Michael White
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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.
Author(s): Gourdeau F, White MC
Publication type: Article
Publication status: Published
Journal: Journal of Mathematical Analysis and Applications
Print publication date: 15/02/2012
ISSN (print): 0022-247X
ISSN (electronic): 1096-0813
Publisher: Academic Press
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