Generalized Polygons:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1998
|
| Schriftenreihe: | Monographs in Mathematics
93 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is intended to be an introduction to the fascinating theory ofgeneralized polygons for both the graduate student and the specialized researcher in the field. It gathers together a lot of basic properties (some of which are usually referred to in research papers as belonging to folklore) and very recent and sometimes deep results. I have chosen a fairly strict geometrical approach, which requires some knowledge of basic projective geometry. Yet, it enables one to prove some typically group-theoretical results such as the determination of the automorphism groups of certain Moufang polygons. As such, some basic group-theoretical knowledge is required of the reader. The notion of a generalized polygon is a relatively recent one. But it is one of the most important concepts in incidence geometry. Generalized polygons are the building bricks of Tits buildings. They are the prototypes and precursors of more general geometries such as partial geometries, partial quadrangles, semi-partial ge ometries, near polygons, Moore geometries, etc. The main examples of generalized polygons are the natural geometries associated with groups of Lie type of relative rank 2. This is where group theory comes in and we come to the historical raison d'etre of generalized polygons. In 1959 Jacques Tits discovered the simple groups of type 3D by classifying the 4 trialities with at least one absolute point of a D -geometry. The method was 4 predominantly geometric, and so not surprisingly the corresponding geometries (the twisted triality hexagons) came into play. Generalized hexagons were born |
| Beschreibung: | 1 Online-Ressource (XV, 502 p) |
| ISBN: | 9783034888271 9783764358648 |
| ISSN: | 1017-0480 |
| DOI: | 10.1007/978-3-0348-8827-1 |
Internformat
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Datensatz im Suchindex
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| any_adam_object | |
| author | Maldeghem, Hendrik |
| author_facet | Maldeghem, Hendrik |
| author_role | aut |
| author_sort | Maldeghem, Hendrik |
| author_variant | h m hm |
| building | Verbundindex |
| bvnumber | BV042422241 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863713151 (DE-599)BVBBV042422241 |
| dewey-full | 516.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8827-1 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034888271 9783764358648 |
| issn | 1017-0480 |
| language | English |
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| spelling | Maldeghem, Hendrik Verfasser aut Generalized Polygons by Hendrik Maldeghem Basel Birkhäuser Basel 1998 1 Online-Ressource (XV, 502 p) txt rdacontent c rdamedia cr rdacarrier Monographs in Mathematics 93 1017-0480 This book is intended to be an introduction to the fascinating theory ofgeneralized polygons for both the graduate student and the specialized researcher in the field. It gathers together a lot of basic properties (some of which are usually referred to in research papers as belonging to folklore) and very recent and sometimes deep results. I have chosen a fairly strict geometrical approach, which requires some knowledge of basic projective geometry. Yet, it enables one to prove some typically group-theoretical results such as the determination of the automorphism groups of certain Moufang polygons. As such, some basic group-theoretical knowledge is required of the reader. The notion of a generalized polygon is a relatively recent one. But it is one of the most important concepts in incidence geometry. Generalized polygons are the building bricks of Tits buildings. They are the prototypes and precursors of more general geometries such as partial geometries, partial quadrangles, semi-partial ge ometries, near polygons, Moore geometries, etc. The main examples of generalized polygons are the natural geometries associated with groups of Lie type of relative rank 2. This is where group theory comes in and we come to the historical raison d'etre of generalized polygons. In 1959 Jacques Tits discovered the simple groups of type 3D by classifying the 4 trialities with at least one absolute point of a D -geometry. The method was 4 predominantly geometric, and so not surprisingly the corresponding geometries (the twisted triality hexagons) came into play. Generalized hexagons were born Mathematics Geometry, algebraic Algebraic Geometry Mathematik Polygon (DE-588)4175197-8 gnd rswk-swf Verallgemeinertes Polygon (DE-588)4523359-7 gnd rswk-swf Polygon (DE-588)4175197-8 s 1\p DE-604 Verallgemeinertes Polygon (DE-588)4523359-7 s 2\p DE-604 https://doi.org/10.1007/978-3-0348-8827-1 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 | Maldeghem, Hendrik Generalized Polygons Mathematics Geometry, algebraic Algebraic Geometry Mathematik Polygon (DE-588)4175197-8 gnd Verallgemeinertes Polygon (DE-588)4523359-7 gnd |
| subject_GND | (DE-588)4175197-8 (DE-588)4523359-7 |
| title | Generalized Polygons |
| title_auth | Generalized Polygons |
| title_exact_search | Generalized Polygons |
| title_full | Generalized Polygons by Hendrik Maldeghem |
| title_fullStr | Generalized Polygons by Hendrik Maldeghem |
| title_full_unstemmed | Generalized Polygons by Hendrik Maldeghem |
| title_short | Generalized Polygons |
| title_sort | generalized polygons |
| topic | Mathematics Geometry, algebraic Algebraic Geometry Mathematik Polygon (DE-588)4175197-8 gnd Verallgemeinertes Polygon (DE-588)4523359-7 gnd |
| topic_facet | Mathematics Geometry, algebraic Algebraic Geometry Mathematik Polygon Verallgemeinertes Polygon |
| url | https://doi.org/10.1007/978-3-0348-8827-1 |
| work_keys_str_mv | AT maldeghemhendrik generalizedpolygons |