Seidon Alsaody

Abstract:

Among simple algebraic groups or, more generally, affine group schemes, those of exceptional type stand out. They do, almost by definition, not lend themselves to a systematic study. Yet they arise as automorphism groups of certain non-associative algebras, or as isometry groups of related forms. These algebras have various kinds of algebraic deformations that have been known for a long time

As it turns out, these deformations correspond precisely to twists by torsors under these exceptional groups. In one direction, this gives us a new way to study the algebras. In the other direction, the algebras can now be used to understand the exceptional groups themselves as G-torsors over certain schemes, where G is a smaller group. In this talk, I will introduce this approach and survey the results obtained so far.