L²-Betti numbers and Plancherel measure

2013/07/01 by Henrik Densing Petersen, Petersen, Henrik Densing, Alain Valette +1
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1307.0379

openalex publication_date 2013/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute L²-Betti numbers of postliminal, locally compact, unimodular groups in terms of ordinary dimensions of reduced cohomology with coefficients in irreducible unitary representations and the Plancherel measure. This allows us to compute the L²-Betti numbers for semi-simple Lie groups with finite center, simple algebraic groups over local fields, and automorphism groups of locally finite trees acting transitively on the boundary.

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