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Feldname	Details
Dewey Class	512.2
Titel	Linear Algebraic Groups ([EBook] /) / by James E. Humphreys.
Verfasser	Humphreys, James E.
Other name(s)	SpringerLink (Online service)
Veröffentl	New York, NY : : Springer New York, , 1975.
Physical Details	XVI, 248 p. : online resource.
Reihe	Graduate texts in mathematics 0072-5285 ; ; 21
ISBN	9781468494433
Summary Note	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 note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4684-9443-3
LINKS ZU 'VERWANDTEN WERKEN	Schlagwörter: . Group theory . Group Theory and Generalizations . Mathematics . Authors: Humphreys, James E. . Corporate Authors: SpringerLink (Online service) . Series: Graduate texts in mathematics . GTM . Classification: 512.2 .

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Linear Algebraic Groups

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