Lie Algebras Generated by Extremal Elements
Identifieur interne : 000061 ( France/Analysis ); précédent : 000060; suivant : 000062Lie Algebras Generated by Extremal Elements
Auteurs : Arjeh M. Cohen [Pays-Bas] ; Anja Steinbach [Allemagne] ; Rosane Ushirobira [France] ; David WalesSource :
- Journal of Algebra [ 0021-8693 ] ; 2001.
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.
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DOI: 10.1006/jabr.2000.8508
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Cohen</name><affiliation wicri:level="1"><country wicri:rule="url">Pays-Bas</country><wicri:regionArea>Faculteit Wiskunde en Informatica, TUE, P.O. 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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.</div></front></TEI><affiliations><list><country><li>Allemagne</li><li>France</li><li>Pays-Bas</li></country><region><li>Bourgogne</li><li>Bourgogne-Franche-Comté</li></region><settlement><li>Dijon</li></settlement><orgName><li>Université de Bourgogne</li></orgName></list><tree><noCountry><name sortKey="Wales, David" sort="Wales, David" uniqKey="Wales D" first="David" last="Wales">David Wales</name></noCountry><country name="Pays-Bas"><noRegion><name sortKey="Cohen, Arjeh M" sort="Cohen, Arjeh M" uniqKey="Cohen A" first="Arjeh M" last="Cohen">Arjeh M. Cohen</name></noRegion></country><country name="Allemagne"><noRegion><name sortKey="Steinbach, Anja" sort="Steinbach, Anja" uniqKey="Steinbach A" first="Anja" last="Steinbach">Anja Steinbach</name></noRegion></country><country name="France"><region name="Bourgogne-Franche-Comté"><name sortKey="Ushirobira, Rosane" sort="Ushirobira, Rosane" uniqKey="Ushirobira R" first="Rosane" last="Ushirobira">Rosane Ushirobira</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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