Graduate Number Theory Seminar
Robert Krzyzanowski
UIC
Linearization of affine algebraic groups
Abstract: In this talk we aim to understand a convenient theorem on affine algebraic groups.
Namely, given any such group, we can embed it into GL(n) for some (n).
In the same way that Cayley's theorem in group theory reduces the study of abstract groups to
those of permutation groups, this theorem transforms the study of affine algebraic groups to linear groups
Although the arbitrariness of the chosen representation makes it sometimes difficult to exploit,
we can use this approach as a technical aid in certain proofs (e.g. exploit the special behaviors of eigenvalues).
Wednesday September 1, 2010 at 3:00 PM in SEO 427