HARVARD
MATH 126 -
Lecture 10
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Conjugacy of Cartan subalgebras.Math 126 Lecture 10Motivation from the unitary groups.yMotivation from compact Lie groups.Proof via a variational principle.GoalConsequences ofDerivations of semi-simple Lie algebras.A key lemma.Conjugacy.An alternative definition of a CSA.thenRecall:The image of a CSA under a surjection is a CSA.The inverse image of a CSA.Conjugacy of CSAs in the solvable case.Recall thatBack to the proof of the conjugacy of CSAs in the solvable case by induction on the dimension.We are reduced to the caseToral subalgebras.Toral subalgebras and Cartan subalgebras.Roots.Facts about roots.Toral subalgebras and CSAs.We are provingWe are provingWe are provingCompletion of the proof ofProof
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