The Generalised Jacobson-Morosov Theorem

Peter O'Sullivan author

Format:Paperback

Publisher:American Mathematical Society

Published:30th Aug '10

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The Generalised Jacobson-Morosov Theorem cover

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.

ISBN: 9780821848951

Dimensions: unknown

Weight: 456g

120 pages