Linear Algebraic Groups
Published on 22. June 2012
Book
Paperback/Softback
XVI, 248 pages
978-1-4684-9445-7 (ISBN)
Description
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).
Reviews / Votes
J.E. Humphreys
Linear Algebraic Groups
"Exceptionally well-written and ideally suited either for independent reading or as a graduate level text for an introduction to everything about linear algebraic groups."- MATHEMATICAL REVIEWS
More details
Series
Edition
Softcover reprint of the original 1st ed. 1975
Language
English
Place of publication
New York
United States
Target group
Primary & secondary/elementary & high school
Graduate
Illustrations
XVI, 248 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 15 mm
Weight
411 gr
ISBN-13
978-1-4684-9445-7 (9781468494457)
DOI
10.1007/978-1-4684-9443-3
Schweitzer Classification
Other editions
Additional editions
James E. Humphreys
Linear Algebraic Groups
E-Book
12/2012
1st Edition
Springer
€69.99
Available for download
Content
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.