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Fall 2014
Chevalley's theorem on the conjugacy of split Cartan subalgebras is one of the cornerstones of the theory of simple finite dimensional Lie algebras over a field of characteristic 0. Indeed, this theorem affords the most elegant proof that the root system is an invariant of the Lie algebra. The...
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Fall 2013
When computing the essential dimension of an algebraic group G defined over a field k, finding lower bounds is generally a much more difficult problem than finding upper bounds. For simple algebraic groups G of adjoint type, Chernousov-Serre developed a general method for computing lower bounds...
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Spring 2010
The purpose of this thesis is to give a classification of anisotropic algebraic groups over number fields of higher real rank. This will complete the classification of algebraic groups over number fields of higher real rank, which was begun by V. Chernousov, L. Lifschitz and D.W. Morris in their...