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SUMMARY:The Jacobson-Morozov Theorem and Complete Reduciblity of Lie subal
 gebras - Adam Thomas\, University of Cambridge
DTSTART:20150527T153000Z
DTEND:20150527T163000Z
UID:TALK59492@talks.cam.ac.uk
CONTACT:David Stewart
DESCRIPTION:The well-known Jacobson-Morozov Theorem states that every nilp
 otent element of a complex semisimple Lie algebra $\\mathfrak{g} = Lie(G)$
  can be uniquely embedded in an $\\mathfrak{sl}_2$-subalgebra\, up to conj
 ugacy 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 algeb
 raically closed field of characteristic $p > 0$. I will discuss recent joi
 nt 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 $\\mat
 hfrak{g}$ 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)$.
LOCATION:MR12
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