Details:
Title  Computing split maximal toral subalgebras of Lie algebras over fields of small characteristic  Author(s)  Dan Roozemond  Type  Article in Journal  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 (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.  Keywords  Lie algebras, Isomorphism problems, Toral subalgebras, Algorithms, Groups of Lie type  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S074771711200137X 
Language  English  Journal  Journal of Symbolic Computation  Volume  50  Number  0  Pages  335  349  Year  2013  Edition  0  Translation 
No  Refereed 
No 
