"Volume 207, number 973 (third of 5 numbers)."

Includes bibliographical references and index.

Introduction Notation and terminology Chapter 1. Affine group schemes over a field of characteristic zero Chapter 2. Universal and minimal reductive homomorphisms Chapter 3. Groups with action of a proreductive group Chapter 4. Families of minimal reductive homomorphisms

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"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, Andr�ae 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."--Publisher's description.

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

Mode of access : World Wide Web

Description based on print version record.