Extremal presentations for classical Lie algebras

J.C.H.W. Panhuis, in 't, E.J. Postma, D.A. Roozemond

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

2 Citaten (Scopus)

Samenvatting

The long-root elements in Lie algebras of Chevalley type have been well studied and can be characterized as extremal elements, that is, elements x such that the image of (adx)2 lies in the subspace spanned by x. In this paper, assuming an algebraically closed base field of characteristic not 2, we find presentations of the Lie algebras of classical Chevalley type by means of minimal sets of extremal generators. The relations are described by simple graphs on the sets. For example, for Cn the graph is a path of length 2n, and for An the graph is the triangle connected to a path of length n-3.
Originele taal-2Engels
Pagina's (van-tot)295-326
TijdschriftJournal of Algebra
Volume322
Nummer van het tijdschrift2
DOI's
StatusGepubliceerd - 2009

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