Actions and Invariants of Algebraic Groups

Walter Ricardo Ferrer Santos, Alvaro Rittatore

• Publisher: CRC Press
• Year: 2017
• Print ISBN: 9781482239157
• eBook ISBN: 9781351644778
• Edition: 2
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

Actions and Invariants of Algebraic Groups, Second Edition presents a self-contained introduction to geometric invariant theory starting from the basic theory of affine algebraic groups and proceeding towards more sophisticated dimensions." Building on the first edition, this book provides an introduction to the theory by equipping the reader with the tools needed to read advanced research in the field. Beginning with commutative algebra, algebraic geometry and the theory of Lie algebras, the book develops the necessary background of affine algebraic groups over an algebraically closed field, and then moves toward the algebraic and geometric aspects of modern invariant theory and quotients.

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface to the Second Edition
• Preface to the First Edition
• Enumeration of items and cross-references
• 1 Algebraic geometry: basic definitions and results
• 2 Algebraic varieties
• 3 Lie algebras
• 4 Algebraic groups: basic definitions
• 5 Algebraic groups: Lie algebras and representations
• 6 Algebraic groups: Jordan decomposition and applications
• 7 Actions of algebraic groups
• 8 Homogeneous spaces
• 9 Algebraic groups and Lie algebras in characteristic zero
• 10 Reductivity
• 11 Observable subgroups of affine algebraic groups
• 12 Affine homogeneous spaces
• 13 Hilbert’s 14th problem
• 14 Quotient varieties: basic results
• 15 Observable actions of affine algebraic groups
• 16 Quotient varieties: an introduction to geometric invariant theory
• Appendix: basic definitions and results
• Bibliography
• Glossary of Notations
• Author Index
• Index