Actions and invariants of algebraic groups. (2005)

• Record Type: Book
• Further Information: Note: Walter Ferrer Santos, Alvaro Rittatore.
• Other Names: Ferrer Santos, Walter Ricardo; Rittatore, Alvaro
• Contents: ALGEBRAIC GEOMETRY; Introduction; Commutative Algebra; Algebraic subsets of the Affine Space; Algebraic Varieties; Deeper Results on Morphisms; Exercises; ; LIE ALGEBRAS; Introduction; Definitions and Basic Concepts; The Theorems of F. Engel and S. Lie; Semisimple Lie Algebras; Cohomology of Lie Algebras; The Theories of H. Weyl and F. Levi; p-Lie Algebras; Exercises; ; ALGEBRAIC GROUPS: BASIC DEFINITIONS; Introduction; Definitions and Basic Concepts; Subgroups and Homomorphisms; Actions of Affine Groups on Algebraic Varieties; Subgroups and Semidirect Products; Exercises; ; ALGEBRAIC GROUPS: LIE ALGEBRAS AND REPRESENTATIONS; Introduction; Hopf Algebras and Algebraic Groups; Rational G-Modules; Representations of SL(2); Characters and Semi-Invariants; The Lie Algebra Associated to an Affine Algebraic Group; Explicit Computations; Exercises; ; ALGEBRAIC GROUPS: JORDAN DECOMPOSITION AND APPLICATIONS; Introduction; The Jordan Decomposition of a Single Operator; The Jordan Decompostiion of an Algebra Homomorphism and of a Derivation; Jordan Decomposition for Coalgebras; Jordan Decomposition for an Affine Algebraic Group; Unipotency and Semisimplicity; The Solvable and the Unipotent Radical; Structure of Solvable Groups; The Classical Groups; Exercises; ; ACTIONS OF ALGEBRAIC GROUPS; Introduction; Actions: Examples and First Properties; Basic Facts about te Geometry of the Orbits; Categorical and Geometric Quotients; The Subalgebras of Invariants; Induction and Restriction of Representations; Exercises; ; HOMOGENEOUS SPACES; Introduction; Embedding H-Modules inside G-Modules; Definition of Subgroups in Terms of Semi-Invariants; The Coset Space G/H as a Geometric Quotient; Quotients by Normal Subgroups; Applications and Examples; Exercises; ; ALGEBRAIC GROUPS AND LIE ALGEBRAS IN CHARACTERISTIC ZERO; Introduction; Correspondence Between Subgroups and Subalgebras; Algebraic Lie Algebras; Exercises; ; REDUCTIVITY; Introduction; Linear and Geometric Reductivity; Examples of Linearly and Geometrically Reductive Groups; Reductivity and the Structure of the Group; Reductive Groups are Linearly Reductive in Characteristic Zero; Exercises; ; OBSERVABLE SUBGROUPS OF AFFINE ALGEBRAIC GROUPS; Introduction; Basic Definitions; Induction and Observability; Split and Strong Observability; The Geometric Characterization of Observability; Exercises; ; AFFINE HOMOGENEOUS SPACES; Introduction; Geometric Reductivity and Observability; Exact Subgroups; From Quasi-Affine to Affine Homogeneous Spaces; Exactness, Reynolds Operators, Total Integrals; Affine Homogeneous Spaces and Exactness; Affine Homogeneous Spaces and Reductivity; Exactness and Integrals for Unipotent Groups; Exercises; ; HILBERT'S FOURTEENTH PROBLEM; Introduction; A Counterexample to Hilbert's 14th Problem; Reductive Groups and Finite Generation of Invariants; V. Popov's Converse to Nagata's Theorem; Partial Positive Answers to Hilbert's 14th Problem; Geometric characterization of Grosshans Pairs; Exercises; ; QUOTIENTS; Introduction; Actions by Reductive Groups: The Categorical Quotient; Actions by Reductive Groups: The Geometric Quotient; Canonical Forms of Matrices: A Geometric Perspective; Rosenlicht's Theorem; Further Results on Invariants of Finite Groups; Exercises; ; APPENDIX: Basic Definitions and Results; ; Bibliography; Author Index; Glossary of Notation; Index
• Publisher Details: Boca Raton : Chapman & Hall/CRC Press
• Publication Date: 2005
• Extent: 1 online resource (xvi, 454 pages), illustrations
• Subjects: 512/.2; Affine algebraic groups; Invariants; MATHEMATICS -- Group Theory; Affine algebraic groups; Invariants; Electronic books
• Languages: English
• ISBNs: 1420030795; 9781420030792; 9780824758967
• Related ISBNs: 082475896X; 082475896X
• Notes: Note: Includes bibliographical references (pages 433-439) and indexes.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.