## Orbits in Lie Algebras |

**David Vella**

October 20, 2005

1:00 pm

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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