Orbits in Lie Algebras
October 20, 2005
Bailey Hall 102
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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