000 04830nam a22005295i 4500
001 978-1-4612-0941-6
003 DE-He213
005 20210921163821.0
007 cr nn 008mamaa
008 121227s1991 xxu| s |||| 0|eng d
020 _a9781461209416
_9978-1-4612-0941-6
024 7 _a10.1007/978-1-4612-0941-6
_2doi
050 4 _aQA252.3
050 4 _aQA387
072 7 _aPBG
_2bicssc
072 7 _aMAT014000
_2bisacsh
072 7 _aPBG
_2thema
082 0 4 _a512.55
_223
082 0 4 _a512.482
_223
100 1 _aBorel, Armand.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aLinear Algebraic Groups
_h[electronic resource] /
_cby Armand Borel.
250 _a2nd ed. 1991.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c1991.
300 _aXI, 290 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 ;
_v126
505 0 _aAG-Background Material From Algebraic Geometry -- §1. Some Topological Notions -- §2. Some Facts from Field Theory -- §3. Some Commutative Algebra -- §4. Sheaves -- §5. Affine K-Schemes, Prevarieties -- §6. Products; Varieties -- §7. Projective and Complete Varieties -- §8. Rational Functions; Dominant Morphisms -- §9. Dimension -- §10. Images and Fibres of a Morphism -- §11. k-structures on K-Schemes -- §12. k-Structures on Varieties -- §13. Separable points -- §14. Galois Criteria for Rationality -- §15. Derivations and Differentials -- §16. Tangent Spaces -- §17. Simple Points -- §18. Normal Varieties -- References -- I-General Notions Associated With Algebraic Groups -- §1. The Notion of an Algebraic Groups -- §2. Group Closure; Solvable and Nilpotent Groups -- §3. The Lie Algebra of an Algebraic Group -- §4. Jordan Decomposition -- II - Homogeneous Spaces -- §5. Semi-Invariants -- §6. Homogeneous Spaces -- §7. Algebraic Groups in Characteristic Zero -- III Solvable Groups -- §8. Diagonalizable Groups and Tori -- §9. Conjugacy Classes and Centralizers of Semi-Simple Elements -- §10. Connected Solvable Groups -- IV-Borel Subgroups; Reductive Groups -- §11. Borel Subgroups -- §12. Cartan Subgroups; Regular Elements -- §13. The Borel Subgroups Containing a Given Torus -- §14. Root Systems and Bruhat Decomposition in Reductive Groups -- V-Rationality Questions -- §15. Split Solvable Groups and Subgroups -- §16. Groups over Finite Fields -- §17. Quotient of a Group by a Lie Subalgebra -- §18. Cartan Subgroups over the Groundfield. Unirationality. Splitting of Reductive Groups -- §19. Cartan Subgroups of Solvable Groups -- §20. Isotropic Reductive Groups -- §21. Relative Root System and Bruhat Decomposition for Isotropic Reductive Groups -- §22. Central Isogenies -- §23. Examples -- §24. Survey of Some Other Topics -- A. Classification -- B. Linear Representations -- C. Real Reductive Groups -- References for Chapters I to V -- Index of Definition -- Index of Notation.
520 _aThis book is a revised and enlarged edition of "Linear Algebraic Groups", published by W.A. Benjamin in 1969. The text of the first edition has been corrected and revised. Accordingly, this book presents foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. After establishing these basic topics, the text then turns to solvable groups, general properties of linear algebraic groups and Chevally's structure theory of reductive groups over algebraically closed groundfields. The remainder of the book is devoted to rationality questions over non-algebraically closed fields. This second edition has been expanded to include material on central isogenies and the structure of the group of rational points of an isotropic reductive group. The main prerequisite is some familiarity with algebraic geometry. The main notions and results needed are summarized in a chapter with references and brief proofs.
650 0 _aTopological groups.
650 0 _aLie groups.
650 1 4 _aTopological Groups, Lie Groups.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11132
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9781461269540
776 0 8 _iPrinted edition:
_z9780387973708
776 0 8 _iPrinted edition:
_z9781461209423
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v126
856 4 0 _uhttps://doi.org/10.1007/978-1-4612-0941-6
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-BAE
999 _c9531
_d9531