Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- 1 Definitions and Basic Properties
- 2 Examples and Basic Constructions
- 3 Affine Algebraic Groups and Hopf Algebras
- 4 Linear Representations of Algebraic Groups
- 5 Group Theory; the Isomorphism Theorems
- 6 Subnormal Series; Solvable and Nilpotent Algebraic Groups
- 7 Algebraic Groups Acting on Schemes
- 8 The Structure of General Algebraic Groups
- 9 Tannaka Duality; Jordan Decompositions
- 10 The Lie Algebra of an Algebraic Group
- 11 Finite Group Schemes
- 12 Groups of Multiplicative Type; Linearly Reductive Groups
- 13 Tori Acting on Schemes
- 14 Unipotent Algebraic Groups
- 15 Cohomology and Extensions
- 16 The Structure of Solvable Algebraic Groups
- 17 Borel Subgroups and Applications
- 18 The Geometry of Algebraic Groups
- 19 Semisimple and Reductive Groups
- 20 Algebraic Groups of Semisimple Rank One
- 21 Split Reductive Groups
- 22 Representations of Reductive Groups
- 23 The Isogeny and Existence Theorems
- 24 Construction of the Semisimple Groups
- 25 Additional Topics
- Appendix A Review of Algebraic Geometry
- Appendix B Existence of Quotients of Algebraic Groups
- Appendix C Root Data
- References
- Index
16 - The Structure of Solvable Algebraic Groups
Published online by Cambridge University Press: 25 October 2017
Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- 1 Definitions and Basic Properties
- 2 Examples and Basic Constructions
- 3 Affine Algebraic Groups and Hopf Algebras
- 4 Linear Representations of Algebraic Groups
- 5 Group Theory; the Isomorphism Theorems
- 6 Subnormal Series; Solvable and Nilpotent Algebraic Groups
- 7 Algebraic Groups Acting on Schemes
- 8 The Structure of General Algebraic Groups
- 9 Tannaka Duality; Jordan Decompositions
- 10 The Lie Algebra of an Algebraic Group
- 11 Finite Group Schemes
- 12 Groups of Multiplicative Type; Linearly Reductive Groups
- 13 Tori Acting on Schemes
- 14 Unipotent Algebraic Groups
- 15 Cohomology and Extensions
- 16 The Structure of Solvable Algebraic Groups
- 17 Borel Subgroups and Applications
- 18 The Geometry of Algebraic Groups
- 19 Semisimple and Reductive Groups
- 20 Algebraic Groups of Semisimple Rank One
- 21 Split Reductive Groups
- 22 Representations of Reductive Groups
- 23 The Isogeny and Existence Theorems
- 24 Construction of the Semisimple Groups
- 25 Additional Topics
- Appendix A Review of Algebraic Geometry
- Appendix B Existence of Quotients of Algebraic Groups
- Appendix C Root Data
- References
- Index
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Algebraic GroupsThe Theory of Group Schemes of Finite Type over a Field, pp. 324 - 351Publisher: Cambridge University PressPrint publication year: 2017