Linear semisimple Lie algebras containing an operator with small number of eigenvalues
type: Item
instance of: scholarly article
title: Linear semisimple Lie algebras containing an operator with small number of eigenvalues
zbMATH Open document ID: 0592.17007
DOI: 10.1007/BF01195020
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: Let V be a finite-dimensional vector space over an algebraically closed field of characteristic zero, let \({\mathfrak g}\) be an irreducible Lie algebra contained in End(V), and let f be a semisimple non-zero endomorphism of V lying in \({\mathfrak g}\). The author investigates what can be concluded about \({\mathfrak g}\) from the knowledge of the eigenvalues of f and their multiplicities. In particular, he shows that if \({\mathfrak g}\) is simple and f has exactly \((r+1)\) different eigenvalues, the highest weight of the \({\mathfrak g}\)-module V is the sum of no more than r fundamental weights.
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 3950772
zbMATH Keywords: simple Lie algebra
zbMATH Keywords: eigenvalues
zbMATH Keywords: multiplicities
zbMATH Keywords: highest weight
author: Yu. G. Zarhin
MaRDI profile type: Publication
cites work: Q4095018
cites work: Q5825260
cites work: A characterization of the classical groups
cites work: Lie algebras of Galois groups arising from Hodge-Tate modules
cites work: Continuous cohomology and \(p\)-adic Galois representations
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full work available at URL: https://doi.org/10.1007/bf01195020
OpenAlex ID: W2005625827
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description: scientific article; zbMATH DE number 3950772