Overview

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).

Full Product Details

Author:   James E. Humphreys
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1st ed. 1975. Corr. 5th printing 1998
Volume:   21
Dimensions:   Width: 15.60cm , Height: 1.70cm , Length: 23.40cm
Weight:   1.250kg
ISBN:  

9780387901084

ISBN 10:   0387901086
Pages:   248
Publication Date:   13 May 1975
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of 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.

Reviews

J.E. Humphreys <p>Linear Algebraic Groups <p> 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. a MATHEMATICAL REVIEWS

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

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