Author | Humphreys, James E. author |
---|---|
Title | Linear Algebraic Groups [electronic resource] / by James E. Humphreys |
Imprint | New York, NY : Springer New York, 1975 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-9443-3 |
Descript | XVI, 248 p. online resource |
I. Algebraic Geometry -- 0. Some Commutative Algebra -- 1. Affine and Projective Varieties -- 2. Varieties -- 3. Dimension -- 4. Morphisms -- 5. Tangent Spaces -- 6. Complete Varieties -- II. Affine Algebraic Groups -- 7. Basic Concepts and Examples -- 8. Actions of Algebraic Groups on Varieties -- III. Lie Algebras -- 9. Lie Algebra of an Algebraic Group -- 10. Differentiation -- IV. Homogeneous Spaces -- 11. Construction of Certain Representations -- 12. Quotients -- V. Characteristic 0 Theory -- 13. Correspondence between Groups and Lie Algebras -- 14. Semisimple Groups -- VI. Semisimple and Unipotent Elements -- 15. Jordan-Chevalley Decomposition -- 16. Diagonalizable Groups -- VII. Solvable Groups -- 17. Nilpotent and Solvable Groups -- 18. Semisimple Elements -- 19. Connected Solvable Groups -- 20. One Dimensional Groups -- VIII. Borel Subgroups -- 21. Fixed Point and Conjugacy Theorems -- 22. Density and Connectedness Theorems -- 23. Normalizer Theorem -- IX. Centralizers of Tori -- 24. Regular and Singular Tori -- 25. Action of a Maximal Torus on G/? -- 26. The Unipotent Radical -- X. Structure of Reductive Groups -- 27. The Root System -- 28. Bruhat Decomposition -- 29. Tits Systems -- 30. Parabolic Subgroups -- XI. Representations and Classification of Semisimple Groups -- 31. Representations -- 32. Isomorphism Theorem -- 33. Root Systems of Rank 2 -- XII. Survey of Rationality Properties -- 34. Fields of Definition -- 35. Special Cases -- Appendix. Root Systems -- Index of Terminology -- Index of Symbols