Low-order cohomology of semi-simple Lie groups with applications to continuous tensor products and current groups
type: Item
instance of: scholarly article
title: Low-order cohomology of semi-simple Lie groups with applications to continuous tensor products and current groups
zbMATH Open document ID: 0532.22013
DOI: 10.1007/BF00120481
author: Joachim Erven
author: Bernd-Jürgen Falkowski
published in: Acta Applicandae Mathematicae
publication date: 1983-01-01T00:00:00Z
review text: The paper gives a survey of first and second-order continuous cohomology of groups in view of possible applications. In particular the standard construction for so-called ''factorizable representations of current groups'' is given and concretely realized for the current group of \(SU(1;1)\). The probabilistic aspect of the theory is, however, only briefly mentioned in the paper. The second named author has in the meantime obtained an analogue of the Lévy-Khintchin formula (in terms of cohomology groups) for the classical split rank one groups. Moreover interesting connections of the theory to Furstenberg's work on noncommuting random products and Gangolli's work on Lévy-Schoenberg kernels have come to light. Thus, apart from applications in mathematical physics, continuous cohomology groups also play an important part in abstract probability theory.
Mathematics Subject Classification ID: 22E41
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 81R10
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 43A35
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 22D10
zbMATH DE Number: 3844035
zbMATH Keywords: continuous cohomology of groups
zbMATH Keywords: \(S0_ e(n
zbMATH Keywords: 1)\)
zbMATH Keywords: SU(n) continuous tensor products
zbMATH Keywords: infinitely divisible representations
Wikidata QID: Q115395261
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00120481
OpenAlex ID: W2058885917
description: scientific article; zbMATH DE number 3844035