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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...
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