University of Birmingham > Talks@bham > Birmingham and Warwick Algebra Seminar  >  The Jacobson-Morozov Theorem and complete reducibility of Lie subalgebras

The Jacobson-Morozov Theorem and complete reducibility of Lie subalgebras

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The well-known Jacobson-Morozov Theorem states that every nilpotent element of a complex semisimple Lie algebra Lie(G) can be embedded in an sl_2-subalgebra. Moreover, a result of Kostant shows that this can be done uniquely, up to G-conjugacy. Much work has been done on extending these fundamental results to the modular case when G is a reductive algebraic group over an algebraically closed field of characteristic p > 0. I will discuss joint work with David Stewart, proving that the uniqueness statement of the theorem holds in the modular case precisely when p is larger than h(G), the Coxeter number of G. In doing so, we consider complete reducibility of subalgebras of Lie(G) in the sense of Serre/McNinch.

This talk is part of the Birmingham and Warwick Algebra Seminar series.

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