Extensions of representations of Lie algebras
type: Item
instance of: scholarly article
title: Extensions of representations of Lie algebras
zbMATH Open document ID: 0637.17002
author: John Gerard Ryan
published in: Pacific Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Let \(f: L_ 1\to L_ 2\) be a homomorphism of finite-dimensional Lie algebras over a field of characteristic zero. Let V be a finite- dimensional \(L_ 1\)-module. The author investigates when V embeds as a sub \(L_ 1\)-module of a finite-dimensional \(L_ 2\)-module. One can assume f injective, in which case the author gives conditions which are necessary and sufficient, provided that either \(f(Radical L_ 1)\subset Radical L_ 2\) or \(L_ 1=[L_ 1,L_ 1]\). The methods of proof make heavy use of the Hopf algebra structure on the representative functions on a Lie algebra.
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 4038043
zbMATH Keywords: extensions
zbMATH Keywords: modules of Lie algebras
zbMATH Keywords: characteristic zero
zbMATH Keywords: Hopf algebra structure
zbMATH Keywords: representative functions
reviewed by: Earl J. Taft
MaRDI profile type: Publication
full work available at URL: pjm.1987.127.173
OpenAlex ID: W2015455276
DOI: 10.2140/PJM.1987.127.173
description: scientific article; zbMATH DE number 4038043