University of Birmingham > Talks@bham > Postgraduate Algebra Seminar > sl_2-triples in prime characteristic

sl_2-triples in prime characteristic

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If you have a question about this talk, please contact Rachel Pengelly.

Let K be an algebraically closed field of prime characteristic. 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). The Jacobson-Morozov theorem, and its analogue in prime characteristic, provide a bijection between the orbits of nilpotent elements of the Lie algebra and the orbits of sl_2-triples. I will give some further results for the classical Lie algebras. I will then introduce exceptional Lie algebras and discuss how we consider sl2-triples in these cases.

This talk is part of the Postgraduate Algebra Seminar series.

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