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001 978-1-4684-9443-3
003 DE-He213
005 20210602114659.0
007 cr nn 008mamaa
008 121227s1975 xxu| s |||| 0|eng d
020 _a9781468494433
_9978-1-4684-9443-3
024 7 _a10.1007/978-1-4684-9443-3
_2doi
050 4 _aQA174-183
072 7 _aPBG
_2bicssc
072 7 _aMAT002010
_2bisacsh
072 7 _aPBG
_2thema
082 0 4 _a512.2
_223
100 1 _aHumphreys, James E.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aLinear Algebraic Groups
_h[electronic resource] /
_cby James E. Humphreys.
250 _a1st ed. 1975.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c1975.
300 _aXVI, 248 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v21
505 0 _aI. 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.
520 _aJames 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).
650 0 _aGroup theory.
650 1 4 _aGroup Theory and Generalizations.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11078
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9781468494457
776 0 8 _iPrinted edition:
_z9780387901084
776 0 8 _iPrinted edition:
_z9781468494440
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v21
856 4 0 _uhttps://doi.org/10.1007/978-1-4684-9443-3
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
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