Abstract
We consider the algorithmic problem of computing Cartan subalgebras in Lie algebras over finite fields and algebraic number fields. We present a deterministic polynomial time algorithm for the case when the ground fieldk is sufficiently large. Our method is based on a solution of a linear algebra problem: the task of finding a locally regular element in a subspace of linear transformations. Also, we give a polynomial time algorithm for restricted Lie algebras over arbitrary finite fields. Both methods require an auxiliary procedure for finding non-nilpotent elements in subalgebras. This problem is also treated. Computational experiences are discussed at the end of the paper.
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Research supported in part by Hungarian National Foundation for Scientific Research grants T016503 and F4116
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De Graaf, W., Ivanyos, G. & Rónyai, L. Computing Cartan subalgebras of Lie algebras. AAECC 7, 339–349 (1996). https://doi.org/10.1007/BF01293593
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DOI: https://doi.org/10.1007/BF01293593