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 | 0747-7171 |
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 |
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