University of Birmingham > Talks@bham > Algebra Seminar  > sl_2-triples in classical Lie algebras over fields of positive characteristic

sl_2-triples in classical Lie algebras over fields of positive characteristic

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If you have a question about this talk, please contact Gareth Tracey.

Let K be an algebraically closed field. Given three elements of some Lie algebra over K, we say that these elements form an sl_2-triple if they generate a subalgebra which is a homomorphic image of sl_2(K). In characteristic 0, the Jacobson-Morozov theorem provides a bijection between the orbits of nilpotent elements of the Lie algebra and the orbits of sl_2-triples. In this talk I will discuss the progress made in extending this result to fields of characteristic p. In particular, I will focus on the results in classical Lie algebras, which can be found as subsets of gl_n(K).

This talk is part of the Algebra Seminar series.

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