Computing Chevalley bases in small characteristics

A.M. Cohen; D.A. Roozemond

doi:10.1016/j.jalgebra.2009.04.038

Computing Chevalley bases in small characteristics

A.M. Cohen
, D.A. Roozemond

Discrete Algebra and Geometry

Research output: Contribution to journal › Article › Academic › peer-review

9 Citations (Scopus)

Abstract

Let L be the Lie algebra of a simple algebraic group defined over a field F and let H be a split maximal toral subalgebra of L. Then L has a Chevalley basis with respect to H. If char (F) ¿ 2,3, it is known how to find it. In this paper, we treat the remaining two characteristics. To this end, we present a few new methods, implemented in Magma, which vary from the computation of centralizers of one root space in another to the computation of a specific part of the Lie algebra of derivations of L.

Original language	English
Pages (from-to)	703-721
Journal	Journal of Algebra
Volume	322
Issue number	3
DOIs	https://doi.org/10.1016/j.jalgebra.2009.04.038
Publication status	Published - 2009

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10.1016/j.jalgebra.2009.04.038

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title = "Computing Chevalley bases in small characteristics",

abstract = "Let L be the Lie algebra of a simple algebraic group defined over a field F and let H be a split maximal toral subalgebra of L. Then L has a Chevalley basis with respect to H. If char (F) ¿ 2,3, it is known how to find it. In this paper, we treat the remaining two characteristics. To this end, we present a few new methods, implemented in Magma, which vary from the computation of centralizers of one root space in another to the computation of a specific part of the Lie algebra of derivations of L.",

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AB - Let L be the Lie algebra of a simple algebraic group defined over a field F and let H be a split maximal toral subalgebra of L. Then L has a Chevalley basis with respect to H. If char (F) ¿ 2,3, it is known how to find it. In this paper, we treat the remaining two characteristics. To this end, we present a few new methods, implemented in Magma, which vary from the computation of centralizers of one root space in another to the computation of a specific part of the Lie algebra of derivations of L.

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DO - 10.1016/j.jalgebra.2009.04.038

M3 - Article

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EP - 721

JO - Journal of Algebra

JF - Journal of Algebra

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ER -

Computing Chevalley bases in small characteristics

Abstract

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