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Lie Algebras Generated by Extremal Elements

Identifieur interne : 001247 ( Main/Exploration ); précédent : 001246; suivant : 001248

Lie Algebras Generated by Extremal Elements

Auteurs : Arjeh M. Cohen [Pays-Bas] ; Anja Steinbach [Allemagne] ; Rosane Ushirobira [France] ; David Wales

Source :

Journal of Algebra [ 0021-8693 ] ; 2001.

RBID : ISTEX:BD49D81102CB4979C5F1976B335D91B920EEA3C6

English descriptors

KwdEn :
- Algebra, Algebraic group, Associative, Bilinear form, Bracket, Bracketing, Cartan subalgebra, Central parameter, Chevalley, Chevalley basis, Chevalley type, Extremal, Extremal element, Extremal elements, Extremal generators, Isomorphic, Jacobi, Lemma, Linear combination, Linear span, Long root, Long root element, Long root elements, Long root subgroups, Lowest root element, Minimal number, Module, Monomials, Natural representation, Nite, Nite dimension, Nite number, Nontrivial, Nonzero, Nonzero element, Quadratic modules, Quotient, Reducible, Root element, Root elements, Root groups, Root length, Sanrad, Simple ideals, Simple roots, Subalgebra, Subgroup, Whole algebra.
Teeft :
- Algebra, Algebraic group, Associative, Bilinear form, Bracket, Bracketing, Cartan subalgebra, Central parameter, Chevalley, Chevalley basis, Chevalley type, Extremal, Extremal element, Extremal elements, Extremal generators, Isomorphic, Jacobi, Lemma, Linear combination, Linear span, Long root, Long root element, Long root elements, Long root subgroups, Lowest root element, Minimal number, Module, Monomials, Natural representation, Nite, Nite dimension, Nite number, Nontrivial, Nonzero, Nonzero element, Quadratic modules, Quotient, Reducible, Root element, Root elements, Root groups, Root length, Sanrad, Simple ideals, Simple roots, Subalgebra, Subgroup, Whole algebra.

Abstract

Abstract: We study Lie algebras generated by extremal elements (i.e., elements spanning inner ideals) over a field of characteristic distinct from 2. There is an associative bilinear form on such a Lie algebra; we study its connections with the Killing form. Any Lie algebra generated by a finite number of extremal elements is finite dimensional. The minimal numbers of extremal generators for the Lie algebras of type An (n≥1), Bn (n≥3), Cn (n≥2), Dn (n≥4), En (n=6,7,8), F4 and G2 are shown to be n+1, n+1, 2n, n, 5, 5, and 4 in the respective cases. These results are related to group theoretic ones for the corresponding Chevalley groups.

Url:

https://api.istex.fr/document/BD49D81102CB4979C5F1976B335D91B920EEA3C6/fulltext/pdf

DOI: 10.1006/jabr.2000.8508

Affiliations:

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Le document en format XML

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Lie Algebras Generated by Extremal Elements

Lie Algebras Generated by Extremal Elements

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English descriptors

Abstract

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