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Orbits in Lie Algebras

by

David Vella

October 20, 2005
1:00 pm
Bailey Hall 102


Abstract:

We intend to classify semisimple orbits in a reductive Lie algebra L.  We begin with a brief review of the structure theory for such an algebra via root systems, followed by a discussion of the centralizer of an element.  The discussion will include a number of concrete examples.  Ultimately we will find that there are infinitely many such orbits, one for each point in a fundamental domain for the action of the Weyl group.  Again, we look at specific examples, and compute the dimensions of several orbits.


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