The first edition of this book presented the theory of linear algebraic groups over an algebraically closed field. The second edition, thoroughly revised and expanded, extends the theory over arbitrary fields, which are not necessarily algebraically closed. It thus represents a higher aim. As in the first edition, the book includes a self-contained treatment of the prerequisites from algebraic geometry and commutative algebra, as well as basic results on reductive groups. As a result, the first part of the book can well serve as a text foran introductory graduate course on linear algebraic groups. The material of the first ten chapters of the new edition is roughly the same as that of the first edition. The arrangement of the material is somewhat different, and a few things have been added, such as the basic facts about algebraic varieties and algebraic groups over a ground field, and an elementary testament of Tannaka’stheorem in Chapter 2. Introduces the theory of algebraic groups over an algebraically closed field Second Edition thoroughly revised and expanded, extending the theory over arbitrary fields which are not necessarily algebraically closed Excellent exercises, bibliography and index INDICE: Preface to the Second Edition.- Some Algebraic Geometry.- Linear Algebraic Groups, First Properties.- Commutative Algebraic Groups.- Derivations, Differentials, Lie Algebras.- Topological Properties of Morphisms, Applications.- Parabolic Subgroups, Borel Subgroups, Solvable Groups.- Weyl Group, Roots, Root Datum.- Reductive Groups.- The Isomorphism Theorem.- The Existence Theorem.- More Algebraic Geometry.- F-groups: General Results.- F-tori.- SolvableF-groups.- F-reductive Groups.- Reductive F-groups.- Classification.- Table of Indices.- Bibliography.- Index.
- ISBN: 978-0-8176-4839-8
- Editorial: Birkhaüser
- Encuadernacion: Rústica
- Páginas: 334
- Fecha Publicación: 01/01/2009
- Nº Volúmenes: 1
- Idioma: Inglés
- Inicio /
- MATEMÁTICAS /
- ÁLGEBRA