Induced representations and hypergroup homomorphisms
type: Item
instance of: scholarly article
title: Induced representations and hypergroup homomorphisms
zbMATH Open document ID: 0793.43004
DOI: 10.1007/BF01301531
author: Peter Hermann
published in: Monatshefte für Mathematik
publication date: 1994-03-14T00:00:00Z
full work available at URL: https://eudml.org/doc/178627
review text: Induced representations on hypergroups were introduced by the author [in Math. Z. 211, No. 4, 687-699 (1992; Zbl 0776.43002)] where some difficulties appear which are unknown for groups. For instance, there may exist non-inducible characters, and even the trivial one may fail to be inducible for commutative hypergroups. In the present paper, the author introduces Weil subhypergroups and Weil homomorphisms and studies relations to induced representations. According to the author, a subhypergroup \(H\) of a hypergroup \(K\) is called Weil if \(T_ H(f)(x * H) := \int_ H f(x*t)d\omega_ H(t)\) leads to a well-defined mapping \(T_ H: C_ \infty(K) \to C_ \infty(K/H)\). Moreover, a hypergroup homomorphism is called Weil if its kernel is a Weil subhypergroup. All subgroups and all compact or supernormal subhypergroups have the Weil property, but there exist examples which fail to be Weil. A Weil decomposition formula for Weil homomorphisms is given in this paper. This in particular proves that lifting of representations via Weil homomorphisms is compatible with the inducing process. Moreover, it follows for supernormal subhypergroups \(H\) of a commutative hypergroup \(K\) that characters on \(H\) are inducible to \(K\) if and only if they can be extended to characters on \(K\).
reviewed by: Michael Voit
Mathematics Subject Classification ID: 43A62
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 22D30
Mathematics Subject Classification ID: 43A20
zbMATH DE Number: 508785
zbMATH Keywords: non-inducible characters
zbMATH Keywords: commutative hypergroups
zbMATH Keywords: Weil subhypergroups
zbMATH Keywords: Weil homomorphisms
zbMATH Keywords: induced representations
zbMATH Keywords: supernormal subhypergroups
zbMATH Keywords: Weil decomposition formula
zbMATH Keywords: lifting of representations
MaRDI profile type: Publication
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OpenAlex ID: W2317395969
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description: scientific article; zbMATH DE number 508785