Holomorphic representation theory. I
type: Item
instance of: scholarly article
title: Holomorphic representation theory. I
zbMATH Open document ID: 0829.43017
DOI: 10.1007/BF01446624
published in: Mathematische Annalen
publication date: 1996-01-24T00:00:00Z
full work available at URL: https://eudml.org/doc/165286
review text: The author introduces the concept of a complex Ol'shanskij semigroup \(S = \Gamma(g,W,\pi_1 (G))\). The main result (Sect. 3) consists of a characterization of those unitary representations of a connected Lie group \(G\) which can be extended to a holomorphic representation of an Ol'shanskij semigroup \(S = \Gamma(g,W, \pi_1 (G))\) with \(U(S)_0 \cong G\). A \(C^*\)-algebra \(C^*(S,\alpha)\) is defined for an Ol'shanskij semigroup \(S\) and an absolute value \(\alpha\) on \(S\) such that the representations of this \(C^*\)-algebra correspond to the \(\alpha\)- bounded holomorphic representation of \(S\).
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 43A35
Mathematics Subject Classification ID: 22E45
zbMATH DE Number: 734584
zbMATH Keywords: representation
zbMATH Keywords: Lie group
zbMATH Keywords: Ol'shanskij semigroup
zbMATH Keywords: unitary representations
zbMATH Keywords: connected Lie group
zbMATH Keywords: holomorphic representation
author: Karl-Hermann Neeb
reviewed by: A. K. Guts
MaRDI profile type: Publication
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OpenAlex ID: W4232967054
description: scientific article; zbMATH DE number 734584