TY  - BOOK
AU  - O'Sullivan,Peter
TI  - The generalised Jacobson-Morosov theorem
T2  - Memoirs of the American Mathematical Society, 
SN  - 9781470405878 (online)
AV  - QA179 .O88 2010
U1  - 512/.5 22
PY  - 2010///
CY  - Providence, R.I.
PB  - American Mathematical Society
KW  - Linear algebraic groups
KW  - Group theory
KW  - Commutative rings
KW  - Algebraic varieties
KW  - Geometry, Algebraic
N1  - "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; Access is restricted to licensed institutions; Electronic reproduction; Providence, Rhode Island; American Mathematical Society; 2012
N2  - "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
UR  - http://www.ams.org/memo/0973
UR  - http://dx.doi.org/10.1090/S0065-9266-10-00603-4
ER  -