Computing Chevalley bases in small characteristics

Details Computing Chevalley bases in small characteristics Computing Chevalley bases in small characteristics

2009-01-13

arxiv.org/abs/0901.1717v2

Mathematics

Rings and Algebras

22 pages

Scientific paper

10.1016/j.jalgebra.2009.04.038

Let L be the Lie algebra of a simple algebraic group defined over a field F and let H be a split Cartan subalgebra of L. Then L has a Chevalley basis with respect to H. If the characteristic of F is not 2 or 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 centralisers 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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