Pseudo-reductive groups /:
"Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable for...
Gespeichert in:
Hauptverfasser: | , , |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
[2015]
|
Ausgabe: | Second edition. |
Schriftenreihe: | New mathematical monographs ;
26. |
Schlagworte: | |
Online-Zugang: | Volltext |
Zusammenfassung: | "Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. In this second edition there is new material on relative root systems and Tits systems for general smooth affine groups, including the extension to quasi-reductive groups of famous simplicity results of Tits in the semisimple case. Chapter 9 has been completely rewritten to describe and classify pseudo-split absolutely pseudo-simple groups with a non-reduced root system over arbitrary fields of characteristic 2 via the useful new notion of 'minimal type' for pseudo-reductive groups. Researchers and graduate students working in related areas, such as algebraic geometry, algebraic group theory, or number theory will value this book, as it develops tools likely to be used in tackling other problems"-- |
Beschreibung: | 1 online resource (xxiv, 665 pages) |
Bibliographie: | Includes bibliographical references (pages 656-658) and index. |
ISBN: | 9781316092439 1316092437 9781316320099 131632009X 1316310078 9781316310076 1316323455 9781316323458 1316330133 9781316330135 1316333477 9781316333471 1316326799 9781316326794 |
Internformat
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245 | 1 | 0 | |a Pseudo-reductive groups / |c Brian Conrad, Stanford University, Ofer Gabber, Institut des hautes études scientifiques, Gopal Prasad, University of Michigan. |
250 | |a Second edition. | ||
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520 | |a "Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. In this second edition there is new material on relative root systems and Tits systems for general smooth affine groups, including the extension to quasi-reductive groups of famous simplicity results of Tits in the semisimple case. Chapter 9 has been completely rewritten to describe and classify pseudo-split absolutely pseudo-simple groups with a non-reduced root system over arbitrary fields of characteristic 2 via the useful new notion of 'minimal type' for pseudo-reductive groups. Researchers and graduate students working in related areas, such as algebraic geometry, algebraic group theory, or number theory will value this book, as it develops tools likely to be used in tackling other problems"-- |c Provided by publisher | ||
505 | 0 | |a Preface to the second edition -- Introduction -- Terminology, conventions, and notation -- Part I. Constructions, examples, and structure theory. 1. Overview of pseudo-reductivity ; 2. Root groups and root systems ; 3. Basic structure theory -- Part II. Standard presentations and their applications. 4. Variation of (G', k'/k, T', C) ; 5. Ubiquity of the standard construction ; 6. Classification results -- Part III. General classification and applications. 7. The exotic constructions ; 8. Preparations for classification in characteristics 2 and 3 ; 9. Absolutely pseudo-simple groups in characteristic 2 ; 10. General case ; 11. Applications -- Part IV. Appendices. A. Background in linear algebraic groups ; B. Tits' work on unipotent groups in nonzero characteristic ; C. Rational conjugacy in connected groups -- References -- Index. | |
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adam_text | |
any_adam_object | |
author | Conrad, Brian, 1970- Gabber, Ofer, 1958- Prasad, Gopal |
author_GND | http://id.loc.gov/authorities/names/nr96030974 http://id.loc.gov/authorities/names/n2003010509 http://id.loc.gov/authorities/names/n80058174 |
author_facet | Conrad, Brian, 1970- Gabber, Ofer, 1958- Prasad, Gopal |
author_role | aut aut aut |
author_sort | Conrad, Brian, 1970- |
author_variant | b c bc o g og g p gp |
building | Verbundindex |
bvnumber | localFWS |
callnumber-first | Q - Science |
callnumber-label | QA179 |
callnumber-raw | QA179 .C66 2015eb |
callnumber-search | QA179 .C66 2015eb |
callnumber-sort | QA 3179 C66 42015EB |
callnumber-subject | QA - Mathematics |
collection | ZDB-4-EBA |
contents | Preface to the second edition -- Introduction -- Terminology, conventions, and notation -- Part I. Constructions, examples, and structure theory. 1. Overview of pseudo-reductivity ; 2. Root groups and root systems ; 3. Basic structure theory -- Part II. Standard presentations and their applications. 4. Variation of (G', k'/k, T', C) ; 5. Ubiquity of the standard construction ; 6. Classification results -- Part III. General classification and applications. 7. The exotic constructions ; 8. Preparations for classification in characteristics 2 and 3 ; 9. Absolutely pseudo-simple groups in characteristic 2 ; 10. General case ; 11. Applications -- Part IV. Appendices. A. Background in linear algebraic groups ; B. Tits' work on unipotent groups in nonzero characteristic ; C. Rational conjugacy in connected groups -- References -- Index. |
ctrlnum | (OCoLC)908254430 |
dewey-full | 512/.55 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 512 - Algebra |
dewey-raw | 512/.55 |
dewey-search | 512/.55 |
dewey-sort | 3512 255 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
edition | Second edition. |
format | Electronic eBook |
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genre | Electronic books. |
genre_facet | Electronic books. |
id | ZDB-4-EBA-ocn908254430 |
illustrated | Not Illustrated |
indexdate | 2024-11-27T13:26:36Z |
institution | BVB |
isbn | 9781316092439 1316092437 9781316320099 131632009X 1316310078 9781316310076 1316323455 9781316323458 1316330133 9781316330135 1316333477 9781316333471 1316326799 9781316326794 |
language | English |
oclc_num | 908254430 |
open_access_boolean | |
owner | MAIN DE-863 DE-BY-FWS |
owner_facet | MAIN DE-863 DE-BY-FWS |
physical | 1 online resource (xxiv, 665 pages) |
psigel | ZDB-4-EBA |
publishDate | 2015 |
publishDateSearch | 2015 |
publishDateSort | 2015 |
publisher | Cambridge University Press, |
record_format | marc |
series | New mathematical monographs ; |
series2 | New mathematical monographs ; |
spelling | Conrad, Brian, 1970- author. https://id.oclc.org/worldcat/entity/E39PBJpPJdRwD4QP6MQJ7JG4MP http://id.loc.gov/authorities/names/nr96030974 Pseudo-reductive groups / Brian Conrad, Stanford University, Ofer Gabber, Institut des hautes études scientifiques, Gopal Prasad, University of Michigan. Second edition. Cambridge ; New York : Cambridge University Press, [2015] 1 online resource (xxiv, 665 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier New mathematical monographs ; 26 Print version record. Includes bibliographical references (pages 656-658) and index. "Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. In this second edition there is new material on relative root systems and Tits systems for general smooth affine groups, including the extension to quasi-reductive groups of famous simplicity results of Tits in the semisimple case. Chapter 9 has been completely rewritten to describe and classify pseudo-split absolutely pseudo-simple groups with a non-reduced root system over arbitrary fields of characteristic 2 via the useful new notion of 'minimal type' for pseudo-reductive groups. Researchers and graduate students working in related areas, such as algebraic geometry, algebraic group theory, or number theory will value this book, as it develops tools likely to be used in tackling other problems"-- Provided by publisher Preface to the second edition -- Introduction -- Terminology, conventions, and notation -- Part I. Constructions, examples, and structure theory. 1. Overview of pseudo-reductivity ; 2. Root groups and root systems ; 3. Basic structure theory -- Part II. Standard presentations and their applications. 4. Variation of (G', k'/k, T', C) ; 5. Ubiquity of the standard construction ; 6. Classification results -- Part III. General classification and applications. 7. The exotic constructions ; 8. Preparations for classification in characteristics 2 and 3 ; 9. Absolutely pseudo-simple groups in characteristic 2 ; 10. General case ; 11. Applications -- Part IV. Appendices. A. Background in linear algebraic groups ; B. Tits' work on unipotent groups in nonzero characteristic ; C. Rational conjugacy in connected groups -- References -- Index. English. Linear algebraic groups. http://id.loc.gov/authorities/subjects/sh85077171 Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Groupes linéaires algébriques. Théorie des groupes. MATHEMATICS Algebra General. bisacsh MATHEMATICS Algebra Intermediate. bisacsh Group theory fast Linear algebraic groups fast Reduktive Gruppe gnd http://d-nb.info/gnd/4177313-5 Lineare algebraische Gruppe gnd http://d-nb.info/gnd/4295326-1 Electronic books. Gabber, Ofer, 1958- author. https://id.oclc.org/worldcat/entity/E39PBJcBYGryJtKPk6JtYj8Bfq http://id.loc.gov/authorities/names/n2003010509 Prasad, Gopal, author. http://id.loc.gov/authorities/names/n80058174 has work: Pseudo-reductive groups (Text) https://id.oclc.org/worldcat/entity/E39PCGjJcFTMXC3YdtpTMvpbHP https://id.oclc.org/worldcat/ontology/hasWork Print version: Conrad, Brian, 1970- Pseudo-reductive groups. Second edition 9781107087231 (DLC) 2014029481 (OCoLC)884961951 New mathematical monographs ; 26. http://id.loc.gov/authorities/names/n2003010567 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=961381 Volltext |
spellingShingle | Conrad, Brian, 1970- Gabber, Ofer, 1958- Prasad, Gopal Pseudo-reductive groups / New mathematical monographs ; Preface to the second edition -- Introduction -- Terminology, conventions, and notation -- Part I. Constructions, examples, and structure theory. 1. Overview of pseudo-reductivity ; 2. Root groups and root systems ; 3. Basic structure theory -- Part II. Standard presentations and their applications. 4. Variation of (G', k'/k, T', C) ; 5. Ubiquity of the standard construction ; 6. Classification results -- Part III. General classification and applications. 7. The exotic constructions ; 8. Preparations for classification in characteristics 2 and 3 ; 9. Absolutely pseudo-simple groups in characteristic 2 ; 10. General case ; 11. Applications -- Part IV. Appendices. A. Background in linear algebraic groups ; B. Tits' work on unipotent groups in nonzero characteristic ; C. Rational conjugacy in connected groups -- References -- Index. Linear algebraic groups. http://id.loc.gov/authorities/subjects/sh85077171 Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Groupes linéaires algébriques. Théorie des groupes. MATHEMATICS Algebra General. bisacsh MATHEMATICS Algebra Intermediate. bisacsh Group theory fast Linear algebraic groups fast Reduktive Gruppe gnd http://d-nb.info/gnd/4177313-5 Lineare algebraische Gruppe gnd http://d-nb.info/gnd/4295326-1 |
subject_GND | http://id.loc.gov/authorities/subjects/sh85077171 http://id.loc.gov/authorities/subjects/sh85057512 http://d-nb.info/gnd/4177313-5 http://d-nb.info/gnd/4295326-1 |
title | Pseudo-reductive groups / |
title_auth | Pseudo-reductive groups / |
title_exact_search | Pseudo-reductive groups / |
title_full | Pseudo-reductive groups / Brian Conrad, Stanford University, Ofer Gabber, Institut des hautes études scientifiques, Gopal Prasad, University of Michigan. |
title_fullStr | Pseudo-reductive groups / Brian Conrad, Stanford University, Ofer Gabber, Institut des hautes études scientifiques, Gopal Prasad, University of Michigan. |
title_full_unstemmed | Pseudo-reductive groups / Brian Conrad, Stanford University, Ofer Gabber, Institut des hautes études scientifiques, Gopal Prasad, University of Michigan. |
title_short | Pseudo-reductive groups / |
title_sort | pseudo reductive groups |
topic | Linear algebraic groups. http://id.loc.gov/authorities/subjects/sh85077171 Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Groupes linéaires algébriques. Théorie des groupes. MATHEMATICS Algebra General. bisacsh MATHEMATICS Algebra Intermediate. bisacsh Group theory fast Linear algebraic groups fast Reduktive Gruppe gnd http://d-nb.info/gnd/4177313-5 Lineare algebraische Gruppe gnd http://d-nb.info/gnd/4295326-1 |
topic_facet | Linear algebraic groups. Group theory. Groupes linéaires algébriques. Théorie des groupes. MATHEMATICS Algebra General. MATHEMATICS Algebra Intermediate. Group theory Linear algebraic groups Reduktive Gruppe Lineare algebraische Gruppe Electronic books. |
url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=961381 |
work_keys_str_mv | AT conradbrian pseudoreductivegroups AT gabberofer pseudoreductivegroups AT prasadgopal pseudoreductivegroups |