An embedding theorem between special linear groups over any fields
type: Item
instance of: scholarly article
title: An embedding theorem between special linear groups over any fields
zbMATH Open document ID: 0839.20058
author: Jianguo Zha
published in: Chinese Annals of Mathematics. Series B
publication date: 1996-06-18T00:00:00Z
review text: Let \(k\) and \(K\) be fields of the same characteristic, and \(n\geq 3\). The author proves that any injective homomorphism \(\sigma\) from \(\text{SL}_n(k)\) to \(\text{SL}_n(K)\) is of ``standard type'', i.e. there exist a homomorphism \(\alpha:k\to K\) and a \(Q\in\text{GL}_n(K)\) such that \(\sigma(A)=QA^\alpha Q^{-1}\) or \(\sigma(A)=Q((A^\alpha)')^{-1}Q^{-1}\) for all \(A\in\text{SL}_n(k)\).
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 832249
zbMATH Keywords: standard homomorphisms
zbMATH Keywords: injective homomorphisms
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 832249