Extremal presentations for classical Lie algebras

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

doi:10.1016/j.jalgebra.2009.04.015

Extremal presentations for classical Lie algebras

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

Discrete Algebra and Geometry

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

3 Citaten (Scopus)

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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-2	Engels
Pagina's (van-tot)	295-326
Tijdschrift	Journal of Algebra
Volume	322
Nummer van het tijdschrift	2
DOI's	https://doi.org/10.1016/j.jalgebra.2009.04.015
Status	Gepubliceerd - 2009

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abstract = "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.",

author = "{Panhuis, in 't}, J.C.H.W. and E.J. Postma and D.A. Roozemond",

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AU - Roozemond, D.A.

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AB - 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.

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Extremal presentations for classical Lie algebras

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