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Graduate Texts in Mathematics Ser.: Linear Algebraic Groups by Armand Borel (1991, Hardcover)
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About this product
Product Identifiers
PublisherSpringer New York
ISBN-100387973702
ISBN-139780387973708
eBay Product ID (ePID)141514
Product Key Features
Number of PagesXi, 290 Pages
LanguageEnglish
Publication NameLinear Algebraic Groups
SubjectGroup Theory, Geometry / Algebraic
Publication Year1991
TypeTextbook
AuthorArmand Borel
Subject AreaMathematics
SeriesGraduate Texts in Mathematics Ser.
FormatHardcover
Dimensions
Item Weight47.6 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Edition Number2
Intended AudienceScholarly & Professional
LCCN90-019774
Dewey Edition20
Series Volume Number126
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal512/.86
Edition DescriptionEnlarged edition,Reprint,Revised edition
Table Of ContentAG--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.
SynopsisThis revised, enlarged edition of Linear Algebraic Groups (1969) starts by presenting foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. It then turns to solvable groups, general properties of linear algebraic groups, and Chevally's structure theory of reductive groups over algebraically closed groundfields. It closes with a focus on rationality questions over non-algebraically closed fields., This is a revised and enlarged edition of "Linear Algebraic Groups" (1969). Accordingly, the book presents foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. After establishing these basic topics, the text 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.
LC Classification NumberQA1-939
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