Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
The Generalised Jacobson-Morosov Theorem
 
Peter O’Sullivan University of Sydney, NSW, Australia
The Generalised Jacobson-Morosov Theorem
eBook ISBN:  978-1-4704-0587-8
Product Code:  MEMO/207/973.E
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $43.80
The Generalised Jacobson-Morosov Theorem
Click above image for expanded view
The Generalised Jacobson-Morosov Theorem
Peter O’Sullivan University of Sydney, NSW, Australia
eBook ISBN:  978-1-4704-0587-8
Product Code:  MEMO/207/973.E
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $43.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2072010; 120 pp
    MSC: Primary 20; Secondary 13; 14;

    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
     
     
    • Chapters
    • Introduction
    • Notation and Terminology
    • 1. Affine Group Schemes over a Field of Characteristic Zero
    • 2. Universal and Minimal Reductive Homomorphisms
    • 3. Groups with Action of a Proreductive Group
    • 4. Families of Minimal Reductive Homomorphisms
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2072010; 120 pp
MSC: Primary 20; Secondary 13; 14;

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 \(k\).

  • Chapters
  • Introduction
  • Notation and Terminology
  • 1. Affine Group Schemes over a Field of Characteristic Zero
  • 2. Universal and Minimal Reductive Homomorphisms
  • 3. Groups with Action of a Proreductive Group
  • 4. Families of Minimal Reductive Homomorphisms
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.