Simplicial cohomology of band semigroup algebras
type: Item
instance of: scholarly article
title: Simplicial cohomology of band semigroup algebras
zbMATH Open document ID: 1263.46060
DOI: 10.1017/S0308210510000648
author: Yemon Choi
author: Frédéric Gourdeau
author: Michael C. White
publication date: 2012-09-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1004.2301
Mathematics Subject Classification ID: 46M18
Mathematics Subject Classification ID: 43A10
Mathematics Subject Classification ID: 13D03
zbMATH DE Number: 6076572
zbMATH Keywords: convolution algebra
zbMATH Keywords: Hochschild cohomology
zbMATH Keywords: cyclic cohomology
zbMATH Keywords: band semigroup
MaRDI profile type: Publication
arXiv ID: 1004.2301
published in: Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
review text: A semigroup formed solely by idempotent elements is called a band semigroup. The \(\ell^1\)-convolution algebra on such a semigroup is a Banach algebra. Its simplicial homology, Hochschild and cyclic cohomology are computed with great ingenuity by the three authors of the present article. Partial results were obtained by one of them [\textit{Y. Choi}, Glasg. Math. J. 48, No. 2, 231--245 (2006; Zbl 1112.46056); Houston J. Math. 36, No. 1, 237--260 (2010; Zbl 1217.46031)]. Specifically, the main results are, for a band semigroup \(S\): The cyclic cohomology of \(\ell^1(S)\) is isomorphic in even degrees to the space of continuous traces on \(\ell^1(S)\), and vanishes in odd degrees. On the other hand, the simplicial cohomology of \(\ell^1(S)\) vanishes in positive degrees.
reviewed by: Mihai Putinar
description: scientific article; zbMATH DE number 6076572