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



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Autore: O'Sullivan Peter <1951-> Visualizza persona
Titolo: The generalised Jacobson-Morosov theorem / / Peter O'Sullivan Visualizza cluster
Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , 2010
©2010
Descrizione fisica: 1 online resource (120 p.)
Disciplina: 512/.5
Soggetto topico: Linear algebraic groups
Group theory
Commutative rings
Algebraic varieties
Geometry, Algebraic
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.
Titolo autorizzato: The generalised Jacobson-Morosov theorem  Visualizza cluster
ISBN: 1-4704-0587-3
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910811629903321
Lo trovi qui: Univ. Federico II
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Serie: Memoirs of the American Mathematical Society ; ; Volume 207, Number 973.