Robert Krzyzanowski : Linearization of affine algebraic groups

Posted by , part of the Graduate Number Theory Seminar.

At

Sept. 1, 2010, 3 p.m.

In

SEO 427

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).