Peter O'Sullivan (University of Sydney)
Friday 21st September, 12.05-12.55pm, Carslaw 373
The generalised Jacobson-Morosov theorem
The classical Jacobson-Morosov theorem states that over a field k of characteristic zero, the embedding of the additive group Ga into SL2 is universal among homomorphisms from Ga to a reductive group, in the sense that any such homomorphism factors through the embedding, and any two factorisations are conjugate.
Based on a categorical splitting theorem, Andre and Kahn proved that a similar universal property holds with Ga replaced by an arbitrary algebraic group over k and SL2 by an appropriate limit of reductive groups. In this talk a more geometric approach to this result will be given, using actions of reductive groups on affine schemes.