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The Generalised Jacobson-Morosov Theorem

Peter O'Sullivan

出版	American Mathematical Soc., 2010-08-06
主題	Mathematics / Algebra / LinearMathematics / Geometry / AlgebraicMathematics / Group Theory
ISBN	082184895X9780821848951
URL	http://books.google.com.hk/books?id=OhrVAwAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

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, Andre 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 $k$.