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Cyclic cohomology of Banach algebras of quivers and their inverse semigroups

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

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Abstract

In this paper, we consider the path semigroup l(1)-algebra for a quiver and the inverse semigroup l(1)-algebra of a quiver, the latter of which can be used in the construction of Cuntz-Krieger algebras. The main objectives of the paper are to determine the simplicial and cyclic cohomology groups of these algebras. First, we determine the simplicial and cyclic cohomology of the path algebra of the quiver, showing the simplicial cohomology groups of dimension n vanish for n > 1. We then determine the simplicial and cyclic cohomology of the inverse semigroup algebra. The work uses the Connes-Tzygan long exact sequence. (C) 2014 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: 2015

Volume: 423

Issue: 1

Pages: 208-228

Print publication date: 01/03/2015

Online publication date: 05/10/2014

ISSN (print): 0022-247X

ISSN (electronic): 1096-0813

Publisher: Academic Press

URL: http://dx.doi.org/10.1016/j.jmaa.2014.09.073

DOI: 10.1016/j.jmaa.2014.09.073

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