MARC details
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04830nam a22005295i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
978-1-4612-0941-6 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20210921163821.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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121227s1991 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781461209416 |
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978-1-4612-0941-6 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-1-4612-0941-6 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA252.3 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA387 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBG |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT014000 |
| Source |
bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBG |
| Source |
thema |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512.55 |
| Edition number |
23 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512.482 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Borel, Armand. |
| Relator term |
author. |
| Relator code |
aut |
| -- |
http://id.loc.gov/vocabulary/relators/aut |
| 245 10 - TITLE STATEMENT |
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| Title |
Linear Algebraic Groups |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc |
by Armand Borel. |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
2nd ed. 1991. |
| 264 #1 - |
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| -- |
New York, NY : |
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Springer New York : |
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Imprint: Springer, |
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1991. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
XI, 290 p. |
| Other physical details |
online resource. |
| 336 ## - |
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text |
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txt |
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rdacontent |
| 337 ## - |
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computer |
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c |
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rdamedia |
| 338 ## - |
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online resource |
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cr |
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rdacarrier |
| 347 ## - |
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text file |
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PDF |
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rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Graduate Texts in Mathematics, |
| International Standard Serial Number |
0072-5285 ; |
| Volume number/sequential designation |
126 |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
AG-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 ## - SUMMARY, ETC. |
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| Summary, etc |
This 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 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Topological groups. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Lie groups. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Topological Groups, Lie Groups. |
| -- |
https://scigraph.springernature.com/ontologies/product-market-codes/M11132 |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Display text |
Printed edition: |
| International Standard Book Number |
9781461269540 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Display text |
Printed edition: |
| International Standard Book Number |
9780387973708 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Display text |
Printed edition: |
| International Standard Book Number |
9781461209423 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
Graduate Texts in Mathematics, |
| -- |
0072-5285 ; |
| Volume number/sequential designation |
126 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://doi.org/10.1007/978-1-4612-0941-6">https://doi.org/10.1007/978-1-4612-0941-6</a> |
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ZDB-2-SXMS |
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ZDB-2-BAE |
