Book contents
- Frontmatter
- Contents
- Preface
- List of tables
- Notation
- PART I LINEAR ALGEBRAIC GROUPS
- 1 Basic concepts
- 2 Jordan decomposition
- 3 Commutative linear algebraic groups
- 4 Connected solvable groups
- 5 G-spaces and quotients
- 6 Borel subgroups
- 7 The Lie algebra of a linear algebraic group
- 8 Structure of reductive groups
- 9 The classification of semisimple algebraic groups
- 10 Exercises for Part I
- PART II SUBGROUP STRUCTURE AND REPRESENTATION THEORY OF SEMISIMPLE ALGEBRAIC GROUPS
- PART III FINITE GROUPS OF LIE TYPE
- Appendix A Root systems
- Appendix B Subsystems
- Appendix C Automorphisms of root systems
- References
- Index
7 - The Lie algebra of a linear algebraic group
from PART I - LINEAR ALGEBRAIC GROUPS
Published online by Cambridge University Press: 05 June 2012
Book contents
- Frontmatter
- Contents
- Preface
- List of tables
- Notation
- PART I LINEAR ALGEBRAIC GROUPS
- 1 Basic concepts
- 2 Jordan decomposition
- 3 Commutative linear algebraic groups
- 4 Connected solvable groups
- 5 G-spaces and quotients
- 6 Borel subgroups
- 7 The Lie algebra of a linear algebraic group
- 8 Structure of reductive groups
- 9 The classification of semisimple algebraic groups
- 10 Exercises for Part I
- PART II SUBGROUP STRUCTURE AND REPRESENTATION THEORY OF SEMISIMPLE ALGEBRAIC GROUPS
- PART III FINITE GROUPS OF LIE TYPE
- Appendix A Root systems
- Appendix B Subsystems
- Appendix C Automorphisms of root systems
- 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
- Linear Algebraic Groups and Finite Groups of Lie Type , pp. 44 - 50Publisher: Cambridge University PressPrint publication year: 2011