Linear Algebraic Groups / by James E. Humphreys.

Format:

Book

Author/Creator:

Humphreys, James E., author.

Contributor:

SpringerLink (Online service)

Series:

Graduate texts in mathematics 2197-5612 ; 21.

Graduate Texts in Mathematics, 2197-5612 ; 21

Language:

English

Subjects (All):

Group theory.

Group Theory and Generalizations.

Local Subjects:

Group Theory and Generalizations.

Physical Description:

1 online resource (XVI, 248 pages).

Edition:

First edition 1975.

Contained In:

Springer Nature eBook

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1975.

System Details:

text file PDF

Summary:

James E. Humphreys is presently Professor of Mathematics at the University of Massachusetts at Amherst. Before this, he held the posts of Assistant Professor of Mathematics at the University of Oregon and Associate Professor of Mathematics at New York University. His main research interests include group theory and Lie algebras. He graduated from Oberlin College in 1961. He did graduate work in philosophy and mathematics at Cornell University and later received hi Ph.D. from Yale University if 1966. In 1972, Springer-Verlag published his first book, "Introduction to Lie Algebras and Representation Theory" (graduate Texts in Mathematics Vol. 9).

Contents:

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.

Other Format:

Printed edition:

ISBN:

9781468494433

Access Restriction:

Restricted for use by site license.