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On Hochschild cohomology of the augmentation ideal of a locally compact group

Published online by Cambridge University Press:  01 January 1999

NIELS GRØNBÆK  and
ANTHONY TO-MING LAU
NIELS GRØNBÆK
Affiliation:
Matematisk Afdeling, Københavns Universitet, Universitetsparken 5, DK-2100 København Ø, Denmark, e-mail: gronbaek@math.ku.dk
ANTHONY TO-MING LAU
Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1, e-mail: tlau@vega.math.ualberta.ca
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Abstract

In this paper we study the cohomology groups Hn(I, I*) and Hn([Uscr ], [Uscr ]*) where [Uscr ] is a Banach algebra with a bounded approximate identity and I is a codimension one closed two-sided ideal of [Uscr ]. This is applied to the case when [Uscr ] is the group algebra L1(G) of a locally compact group G and I={f∈L1(G)[mid ] ∫Gf=0}, the augmentation ideal of G. We show that if G is inner amenable, then I is always weakly amenable, i.e. [Hscr ]1(I, I*)={0}.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 126 , Issue 1 , January 1999 , pp. 139 - 148
Copyright
The Cambridge Philosophical Society 1999

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