The Generalised Jacobson-Morosov Theorem

by Peter O'Sullivan

Overview

The author considers homomorphisms $H \to K$ from an affine group scheme $H$ over a field $k$ of characteristic zero to a proreductive group $K$. Using a general categorical splitting theorem, Andre and Kahn proved that for every $H$ there exists such a homomorphism which is universal up to conjugacy. The author gives a purely group-theoretic proof of this result. The classical Jacobson-Morosov theorem is the particular case where $H$ is the additive group over $k$. As well as universal homomorphisms, the author considers more generally homomorphisms $H \to K$ which are minimal, in the sense that $H \to K$ factors through no proper proreductive subgroup of $K$. For fixed $H$, it is shown that the minimal $H \to K$ with $K$ reductive are parametrised by a scheme locally of finite type over $k$.

Product Details

ISBN-13:	9780821848951
Publisher:	American Mathematical Society
Publication date:	08/06/2010
Series:	Memoirs of the American Mathematical Society Series , #207
Pages:	120
Product dimensions:	6.80(w) x 9.90(h) x 0.30(d)