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University of Cambridge > Talks.cam > Algebra and Representation Theory Seminar > The Jacobson-Morozov Theorem and Complete Reduciblity of Lie subalgebras

## The Jacobson-Morozov Theorem and Complete Reduciblity of Lie subalgebrasAdd to your list(s) Download to your calendar using vCal - Adam Thomas, University of Cambridge
- Wednesday 27 May 2015, 16:30-17:30
- MR12.
If you have a question about this talk, please contact David Stewart. The well-known Jacobson-Morozov Theorem states that every nilpotent element of a complex semisimple Lie algebra $\mathfrak{g} = Lie(G)$ can be uniquely embedded in an $\mathfrak{sl}_2$-subalgebra, up to conjugacy by $G$. Much work has been done on extending this fundamental result to the modular case when $G$ is a reductive algebraic group over an algebraically closed field of characteristic $p > 0$. I will discuss recent joint work with David Stewart, proving that 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 reduciblilty of subalgebras of $\mathfrak{g}$ in the sense of Serre/McNinch. For example, we prove that every $\mathfrak{sl}_2$-subalgebra of $\mathfrak{g}$ is completely reducible precisely when $ p > h(G)$. This talk is part of the Algebra and Representation Theory Seminar series. ## This talk is included in these lists:- Algebra and Representation Theory Seminar
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