AMS Bookstore LOGO amslogo
Return to List

AMS TextbooksAMS Applications-related Books

The Generalised Jacobson-Morosov Theorem
Peter O'Sullivan, University of Sydney, NSW, Australia
cover
SEARCH THIS BOOK:

Memoirs of the American Mathematical Society
2010; 120 pp; softcover
Volume: 207
ISBN-10: 0-8218-4895-X
ISBN-13: 978-0-8218-4895-1
List Price: US$69
Individual Members: US$41.40
Institutional Members: US$55.20
Order Code: MEMO/207/973
[Add Item]

Request Permissions

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 \(k\).

Table of Contents

  • Introduction
  • Notation and terminology
  • 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
  • Bibliography
  • Index
Powered by MathJax

  AMS Home | Comments: webmaster@ams.org
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia