The generalised Jacobson-Morosov theorem / Peter O'Sullivan
- O'Sullivan, Peter, 1951-
- Providence, R.I. : American Mathematical Society, 
- Copyright Date:
- Physical Description:
- vii, 120 pages ; 25 cm.
- Memoirs of the American Mathematical Society, 0065-9266 ; no. 973
- 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.
- "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 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.
- 9780821848951 (alk. paper)
082184895X (alk. paper)
- "Volume 207, number 973 (third of 5 numbers)."
- Bibliography Note:
- Includes bibliographical references (page 117) and index.
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