Homomorphisms between symplectic groups
type: Item
instance of: scholarly article
title: Homomorphisms between symplectic groups
zbMATH Open document ID: 0797.20037
author: Shaowu Liu
author: Luqun Wang
published in: Chinese Annals of Mathematics. Series B
publication date: 1994-02-07T00:00:00Z
review text: Let \(F\) and \(F_ 1\) be fields with \(| F| > 5\), and \(n\), \(n_ 1\) be positive integers with \(n \geq n_ 1\). The authors study the homomorphisms between the symplectic groups \(Sp_{2n}(F)\) and \(Sp_{2n_ 1}(F_ 1)\). It is proved that there exists a non-trivial homomorphism from \(Sp_{2n}(F)\) to \(Sp_{2n_ 1}(F_ 1)\) if and only if \(n = n_ 1\), and there exists a non-trivial homomorphism from \(F\) to \(F_ 1\). It is also proved that almost all non-trivial homomorphisms from \(Sp_{2n}(F)\) to \(Sp_{2n}(F_ 1)\) are of standard type except \(n = 2\) and \(\text{char }F = \text{char }F_ 1 = 2\) in which case there may exist a class of ``exceptional'' non-trivial homomorphisms whose forms are given.
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20H20
zbMATH DE Number: 495842
zbMATH Keywords: symplectic groups
zbMATH Keywords: non-trivial homomorphisms
zbMATH Keywords: standard type
MaRDI profile type: Publication
full work available at URL: s11401-004-0495-4
OpenAlex ID: W1983904721
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Wikidata QID: Q125295908
DOI: 10.1007/S11401-004-0495-4
description: scientific article; zbMATH DE number 495842