O'Sullivan, Peter, 1951-
The generalised Jacobson-Morosov theorem / [electronic resource] Peter O'Sullivan. - Providence, R.I. : American Mathematical Society, 2010. - 1 online resource (vii, 120 p.) - Memoirs of the American Mathematical Society, v. 973 0065-9266 (print); 1947-6221 (online); .
"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
"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
9781470405878 (online)
Linear algebraic groups.
Group theory.
Commutative rings.
Algebraic varieties.
Geometry, Algebraic.
QA179 / .O88 2010
512/.5
The generalised Jacobson-Morosov theorem / [electronic resource] Peter O'Sullivan. - Providence, R.I. : American Mathematical Society, 2010. - 1 online resource (vii, 120 p.) - Memoirs of the American Mathematical Society, v. 973 0065-9266 (print); 1947-6221 (online); .
"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
"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
9781470405878 (online)
Linear algebraic groups.
Group theory.
Commutative rings.
Algebraic varieties.
Geometry, Algebraic.
QA179 / .O88 2010
512/.5