Linear Algebraic Groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1998
|
| Schriftenreihe: | Modern Birkhäuser CIassics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | "[The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author [has a] student-friendly style… [The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literature…appear for the first time in a text." –Mathematical Reviews (Review of the Second Edition) "This book is a completely new version of the first edition. The aim of the old book was to present the theory of linear algebraic groups over an algebraically closed field. Reading that book, many people entered the research field of linear algebraic groups. The present book has a wider scope. Its aim is to treat the theory of linear algebraic groups over arbitrary fields. Again, the author keeps the treatment of prerequisites self-contained. The material of the first ten chapters covers the contents of the old book, but the arrangement is somewhat different and there are additions, such as the basic facts about algebraic varieties and algebraic groups over a ground field, as well as an elementary treatment of Tannaka's theorem. These chapters can serve as a text for an introductory course on linear algebraic groups. The last seven chapters are new. They deal with algebraic groups over arbitrary fields. Some of the material has not been dealt with before in other texts, such as Rosenlicht's results about solvable groups in Chapter 14, the theorem of Borel and Tits on the conjugacy over the ground field of maximal split tori in an arbitrary linear algebraic group in Chapter 15, and the Tits classification of simple groups over a ground field in Chapter 17. The book includes many exercises and a subject index." –Zentralblatt Math (Review of the Second Edition) |
| Beschreibung: | 1 Online-Ressource (XII, 334 p) |
| ISBN: | 9780817648404 9780817648398 |
| DOI: | 10.1007/978-0-8176-4840-4 |
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-0-8176-4840-4 |
| format | Electronic eBook |
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| id | DE-604.BV042419165 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9780817648404 9780817648398 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027854582 |
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| physical | 1 Online-Ressource (XII, 334 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1998 |
| publishDateSearch | 1998 |
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| publisher | Birkhäuser Boston |
| record_format | marc |
| series2 | Modern Birkhäuser CIassics |
| spelling | Springer, T. A. Verfasser aut Linear Algebraic Groups by T. A. Springer Boston, MA Birkhäuser Boston 1998 1 Online-Ressource (XII, 334 p) txt rdacontent c rdamedia cr rdacarrier Modern Birkhäuser CIassics "[The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author [has a] student-friendly style… [The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literature…appear for the first time in a text." –Mathematical Reviews (Review of the Second Edition) "This book is a completely new version of the first edition. The aim of the old book was to present the theory of linear algebraic groups over an algebraically closed field. Reading that book, many people entered the research field of linear algebraic groups. The present book has a wider scope. Its aim is to treat the theory of linear algebraic groups over arbitrary fields. Again, the author keeps the treatment of prerequisites self-contained. The material of the first ten chapters covers the contents of the old book, but the arrangement is somewhat different and there are additions, such as the basic facts about algebraic varieties and algebraic groups over a ground field, as well as an elementary treatment of Tannaka's theorem. These chapters can serve as a text for an introductory course on linear algebraic groups. The last seven chapters are new. They deal with algebraic groups over arbitrary fields. Some of the material has not been dealt with before in other texts, such as Rosenlicht's results about solvable groups in Chapter 14, the theorem of Borel and Tits on the conjugacy over the ground field of maximal split tori in an arbitrary linear algebraic group in Chapter 15, and the Tits classification of simple groups over a ground field in Chapter 17. The book includes many exercises and a subject index." –Zentralblatt Math (Review of the Second Edition) Mathematics Algebra Geometry, algebraic Group theory Matrix theory Number theory Linear and Multilinear Algebras, Matrix Theory Group Theory and Generalizations Algebraic Geometry Number Theory Mathematik Lineare algebraische Gruppe (DE-588)4295326-1 gnd rswk-swf Algebraische Gruppe (DE-588)4001164-1 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Lineare algebraische Gruppe (DE-588)4295326-1 s Algebraische Geometrie (DE-588)4001161-6 s 1\p DE-604 Algebraische Gruppe (DE-588)4001164-1 s 2\p DE-604 https://doi.org/10.1007/978-0-8176-4840-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Springer, T. A. Linear Algebraic Groups Mathematics Algebra Geometry, algebraic Group theory Matrix theory Number theory Linear and Multilinear Algebras, Matrix Theory Group Theory and Generalizations Algebraic Geometry Number Theory Mathematik Lineare algebraische Gruppe (DE-588)4295326-1 gnd Algebraische Gruppe (DE-588)4001164-1 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4295326-1 (DE-588)4001164-1 (DE-588)4001161-6 |
| title | Linear Algebraic Groups |
| title_auth | Linear Algebraic Groups |
| title_exact_search | Linear Algebraic Groups |
| title_full | Linear Algebraic Groups by T. A. Springer |
| title_fullStr | Linear Algebraic Groups by T. A. Springer |
| title_full_unstemmed | Linear Algebraic Groups by T. A. Springer |
| title_short | Linear Algebraic Groups |
| title_sort | linear algebraic groups |
| topic | Mathematics Algebra Geometry, algebraic Group theory Matrix theory Number theory Linear and Multilinear Algebras, Matrix Theory Group Theory and Generalizations Algebraic Geometry Number Theory Mathematik Lineare algebraische Gruppe (DE-588)4295326-1 gnd Algebraische Gruppe (DE-588)4001164-1 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Mathematics Algebra Geometry, algebraic Group theory Matrix theory Number theory Linear and Multilinear Algebras, Matrix Theory Group Theory and Generalizations Algebraic Geometry Number Theory Mathematik Lineare algebraische Gruppe Algebraische Gruppe Algebraische Geometrie |
| url | https://doi.org/10.1007/978-0-8176-4840-4 |
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