Memoirs of the American Mathematical Society 2010; 120 pp; softcover Volume: 207 ISBN10: 082184895X ISBN13: 9780821848951 List Price: US$73 Individual Members: US$43.80 Institutional Members: US$58.40 Order Code: MEMO/207/973
 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, André and Kahn proved that for every \(H\) there exists such a homomorphism which is universal up to conjugacy. The author gives a purely grouptheoretic proof of this result. The classical JacobsonMorosov 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 \(k\). Table of Contents  Introduction
 Notation and terminology
 Affine Group schemes over a field of characteristic zero
 Universal and minimal reductive homomorphisms
 Groups with action of a proreductive group
 Families of minimal reductive homomorphisms
 Bibliography
 Index
