Daws, M (2006) Connes-amenability of bidual and weighted semigroup algebras. Mathematica Scandinavica, 99 (2). 217 - 246. ISSN 0025-5521
Abstract
We investigate the notion of Connes-amenability, introduced by Runde in [10], for bidual algebras and weighted semigroup algebras. We provide some simplifications to the notion of a σ W C-virtual diagonal, as introduced in [13], especially in the case of the bidual of an Arens regular Banach algebra. We apply these results to discrete, weighted, weakly cancellative semigroup algebras, showing that these behave in the same way as C*-algebras with regards Connes-amenability of the bidual algebra. We also show that for each one of these cancellative semigroup algebras l 1(S, ω), we have that l1 (S, ω) is Connes-amenable (with respect to the canonical predual c0(S)) if and only if l1 (S, ω) is amenable, which is in turn equivalent to S being an amenable group, and the weight satisfying a certain restrictive condition. This latter point was first shown by Grønbæk in [6], but we provide a unified proof. Finally, we consider the homological notion of injectivity, and show that here, weighted semigroup algebras do not behave like C*-algebras.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2006, Institut for Matematik, Aarhus Universitet. This is an author produced version of a paper published in Mathematica Scandinavica. Uploaded with permission from the publisher. |
Keywords: | Discrete Convolution-Algebras; Dual Banach-Algebras; Virtual Diagonals; Predual Bimodule |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Dec 2013 11:08 |
Last Modified: | 20 Feb 2024 16:54 |
Published Version: | http://www.mscand.dk/ |
Status: | Published |
Publisher: | Institut for Matematik, Aarhus Universitet |
Identification Number: | 10.7146/math.scand.a-15010 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:77170 |