Record Nr.

UNINA9910788859203321

Autore

O'Sullivan Peter <1951->

Titolo

The generalised Jacobson-Morosov theorem / / Peter O'Sullivan

Pubbl/distr/stampa


Providence, Rhode Island : , : American Mathematical Society, , 2010
©2010

ISBN

1-4704-0587-3

Descrizione fisica

1 online resource (120 p.)

Collana

Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 207, Number 973

Disciplina

512/.5

Soggetti

Linear algebraic groups

Group theory

Commutative rings

Algebraic varieties

Geometry, Algebraic

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

"Volume 207, Number 973 (third of 5 numbers)."

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

""Contents""; ""Introduction""; ""Notation and Terminology""; ""Chapter 1. Affine Group Schemes over a Field of Characteristic Zero""; ""1.1. Groups""; ""1.2. Representations""; ""1.3. Spaces of homomorphisms""; ""Chapter 2. Universal and Minimal Reductive Homomorphisms""; ""2.1. Reductive homomorphisms""; ""2.2. Universal reductive homomorphisms""; ""2.3. Minimal reductive homomorphisms""; ""Chapter 3. Groups with Action of a Proreductive Group""; ""3.1. Simply connected groups""; ""3.2. Groups with action of a group""; ""3.3. Equivariant homomorphisms""

""Chapter 4. Families of Minimal Reductive Homomorphisms""""4.1. Stratifications and constructible subsets""; ""4.2. Reductive group schemes""; ""4.3. Universal families""; ""Bibliography""; ""Index""

Sommario/riassunto

"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, Andrâe 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.