Homological properties of Fourier algebras on homogeneous spaces
type: Item
instance of: scholarly article
title: Homological properties of Fourier algebras on homogeneous spaces
zbMATH Open document ID: 1219.43008
author: N. Shravan Kumar
author: K. Parthasarathy
published in: Archiv der Mathematik
publication date: 2011-06-01T00:00:00Z
review text: After the pioneering work of B. E. Johnson, J. L. Taylor and A. Y. Helemskii on the homological properties of the Fourier algebra \(A(G)\), the topic again got revived through the recent papers of Wood, Forrest, Spronk, Samei, Runde and others. Biprojectivity, biflatness and the operator analogues of these have been studied for the Fourier algebra \(A(G)\) of a locally compact group \(G\). In this interesting note the authors carry out the analogous questions to the Fourier algebra \(A(G/K)\), where \(K\) is a compact subgroup of the locally compact group \(G\). The authors prove that \(A(G/K)\) is operator biprojective if and only if \(K\) is open (or equivalently \(G/K\) is discrete), in Section 4. Completely complemented ideals in \(A(G/K)\) are characterised in Section 5. In the cited work \textit{V. Runde} [Arch. Math. 92, 525--530 (2009; Zbl 1178.22009)] has given a necessary condition for \(A(G)\) to be biflat and biprojective. The authors extend these results to \(A(G/K)\) in the last section of the paper. In particular the authors prove that if \(A(G/K)\) is operator projective then \(K\) is open and in this case \(G\) does not contain the free group on two generators as a closed subgroup.
reviewed by: Madathum K. Viswanath
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 46M18
zbMATH DE Number: 5902950
zbMATH Keywords: Fourier algebra
zbMATH Keywords: homological properties
zbMATH Keywords: biprojective
zbMATH Keywords: biflatness
zbMATH Keywords: free group on two generators
MaRDI profile type: Publication
full work available at URL: s00013-011-0236-3
OpenAlex ID: W2019207811
cites work: Banach algebras and automatic continuity
cites work: L'algèbre de Fourier d'un groupe localement compact
cites work: Fourier analysis on coset spaces
cites work: Convolutions on compact groups and Fourier algebras of coset spaces
cites work: Cohomology and the Operator Space Structure of the Fourier Algebra and its Second Dual
cites work: Weak spectral synthesis in Fourier algebras of coset spaces
cites work: Weak spectral synthesis in commutative Banach algebras
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cites work: Malliavin's theorem for weak synthesis on nonabelian groups
cites work: Biflatness and biprojectivity of the Fourier algebra
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DOI: 10.1007/S00013-011-0236-3
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description: scientific article; zbMATH DE number 5902950