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arXiv · 1108.2932

Computing Split Maximal Toral Subalgebras of Lie algebras over Fields of Small Characteristic

Dan Roozemond
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Abstract

Important subalgebras of a Lie algebra of an algebraic group are its toral subalgebras, or equivalently (over fields of characteristic 0) its Cartan subalgebras. Of great importance among these are ones that are split: their action on the Lie algebra splits completely over the field of definition. While algorithms to compute split maximal toral subalgebras exist and have been implemented [Ryb07, CM09], these algorithms fail when the Lie algebra is defined over a field of characteristic 2 or 3. We present heuristic algorithms that, given a reductive Lie algebra L over a finite field of characteristic 2 or 3, find a split maximal toral subalgebra of L. Together with earlier work [CR09] these algorithms are very useful for the recognition of reductive Lie algebras over such fields.

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Dan Roozemond. 2012-04-24. Computing Split Maximal Toral Subalgebras of Lie algebras over Fields of Small Characteristic. https://arxiv.org/abs/1108.2932

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