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TitleComputing split maximal toral subalgebras of Lie algebras over fields of small characteristic
Author(s) Dan Roozemond
TypeArticle in Journal
AbstractImportant 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 (Ryba, 2007; Cohen and Murray, 2009), 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 (Cohen and Roozemond, 2009) these algorithms are very useful for the recognition of reductive Lie algebras over such fields.
KeywordsLie algebras, Isomorphism problems, Toral subalgebras, Algorithms, Groups of Lie type
URL http://www.sciencedirect.com/science/article/pii/S074771711200137X
JournalJournal of Symbolic Computation
Pages335 - 349
Translation No
Refereed No