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 G_a into SL₂ is universal among homomorphisms from G_a 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 G_a 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.