Moufang Polygons:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2002
|
| Schriftenreihe: | Springer Monographs in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Spherical buildings are certain combinatorial simplicial complexes introduced, at first in the language of "incidence geometries," to provide a systematic geometric interpretation of the exceptional complex Lie groups. (The definition of a building in terms of chamber systems and definitions of the various related notions used in this introduction such as "thick," "residue," "rank," "spherical," etc. are given in Chapter 39. ) Via the notion of a BN-pair, the theory turned out to apply to simple algebraic groups over an arbitrary field. More precisely, to any absolutely simple algebraic group of positive relative rank £ is associated a thick irreducible spherical building of the same rank (these are the algebraic spherical buildings) and the main result of Buildings of Spherical Type and Finite BN-Pairs [101] is that the converse, for £ ::::: 3, is almost true: (1. 1) Theorem. Every thick irreducible spherical building of rank at least three is classical, algebraic' or mixed. Classical buildings are those defined in terms of the geometry of a classical group (e. g. unitary, orthogonal, etc. of finite Witt index or linear of finite dimension) over an arbitrary field or skew-field. (These are not algebraic if, for instance, the skew-field is of infinite dimension over its center. ) Mixed buildings are more exotic; they are related to groups which are in some sense algebraic groups defined over a pair of fields k and K of characteristic p, where KP eke K and p is two or (in one case) three |
| Beschreibung: | 1 Online-Ressource (X, 535 p) |
| ISBN: | 9783662046890 9783642078330 |
| ISSN: | 1439-7382 |
| DOI: | 10.1007/978-3-662-04689-0 |
Internformat
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| 500 | |a Spherical buildings are certain combinatorial simplicial complexes introduced, at first in the language of "incidence geometries," to provide a systematic geometric interpretation of the exceptional complex Lie groups. (The definition of a building in terms of chamber systems and definitions of the various related notions used in this introduction such as "thick," "residue," "rank," "spherical," etc. are given in Chapter 39. ) Via the notion of a BN-pair, the theory turned out to apply to simple algebraic groups over an arbitrary field. More precisely, to any absolutely simple algebraic group of positive relative rank £ is associated a thick irreducible spherical building of the same rank (these are the algebraic spherical buildings) and the main result of Buildings of Spherical Type and Finite BN-Pairs [101] is that the converse, for £ ::::: 3, is almost true: (1. 1) Theorem. Every thick irreducible spherical building of rank at least three is classical, algebraic' or mixed. Classical buildings are those defined in terms of the geometry of a classical group (e. g. unitary, orthogonal, etc. of finite Witt index or linear of finite dimension) over an arbitrary field or skew-field. (These are not algebraic if, for instance, the skew-field is of infinite dimension over its center. ) Mixed buildings are more exotic; they are related to groups which are in some sense algebraic groups defined over a pair of fields k and K of characteristic p, where KP eke K and p is two or (in one case) three | ||
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Datensatz im Suchindex
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| author | Tits, Jacques |
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| building | Verbundindex |
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| dewey-full | 516 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516 |
| dewey-search | 516 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-04689-0 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662046890 9783642078330 |
| issn | 1439-7382 |
| language | English |
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| physical | 1 Online-Ressource (X, 535 p) |
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| spelling | Tits, Jacques Verfasser aut Moufang Polygons by Jacques Tits, Richard M. Weiss Berlin, Heidelberg Springer Berlin Heidelberg 2002 1 Online-Ressource (X, 535 p) txt rdacontent c rdamedia cr rdacarrier Springer Monographs in Mathematics 1439-7382 Spherical buildings are certain combinatorial simplicial complexes introduced, at first in the language of "incidence geometries," to provide a systematic geometric interpretation of the exceptional complex Lie groups. (The definition of a building in terms of chamber systems and definitions of the various related notions used in this introduction such as "thick," "residue," "rank," "spherical," etc. are given in Chapter 39. ) Via the notion of a BN-pair, the theory turned out to apply to simple algebraic groups over an arbitrary field. More precisely, to any absolutely simple algebraic group of positive relative rank £ is associated a thick irreducible spherical building of the same rank (these are the algebraic spherical buildings) and the main result of Buildings of Spherical Type and Finite BN-Pairs [101] is that the converse, for £ ::::: 3, is almost true: (1. 1) Theorem. Every thick irreducible spherical building of rank at least three is classical, algebraic' or mixed. Classical buildings are those defined in terms of the geometry of a classical group (e. g. unitary, orthogonal, etc. of finite Witt index or linear of finite dimension) over an arbitrary field or skew-field. (These are not algebraic if, for instance, the skew-field is of infinite dimension over its center. ) Mixed buildings are more exotic; they are related to groups which are in some sense algebraic groups defined over a pair of fields k and K of characteristic p, where KP eke K and p is two or (in one case) three Mathematics Algebra Geometry, algebraic Group theory Combinatorics Geometry Algebraic Geometry Group Theory and Generalizations Mathematik Verallgemeinertes Polygon (DE-588)4523359-7 gnd rswk-swf Gebäude Mathematik (DE-588)4123258-6 gnd rswk-swf Verallgemeinertes Polygon (DE-588)4523359-7 s Gebäude Mathematik (DE-588)4123258-6 s 1\p DE-604 Weiss, Richard M. Sonstige oth https://doi.org/10.1007/978-3-662-04689-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Tits, Jacques Moufang Polygons Mathematics Algebra Geometry, algebraic Group theory Combinatorics Geometry Algebraic Geometry Group Theory and Generalizations Mathematik Verallgemeinertes Polygon (DE-588)4523359-7 gnd Gebäude Mathematik (DE-588)4123258-6 gnd |
| subject_GND | (DE-588)4523359-7 (DE-588)4123258-6 |
| title | Moufang Polygons |
| title_auth | Moufang Polygons |
| title_exact_search | Moufang Polygons |
| title_full | Moufang Polygons by Jacques Tits, Richard M. Weiss |
| title_fullStr | Moufang Polygons by Jacques Tits, Richard M. Weiss |
| title_full_unstemmed | Moufang Polygons by Jacques Tits, Richard M. Weiss |
| title_short | Moufang Polygons |
| title_sort | moufang polygons |
| topic | Mathematics Algebra Geometry, algebraic Group theory Combinatorics Geometry Algebraic Geometry Group Theory and Generalizations Mathematik Verallgemeinertes Polygon (DE-588)4523359-7 gnd Gebäude Mathematik (DE-588)4123258-6 gnd |
| topic_facet | Mathematics Algebra Geometry, algebraic Group theory Combinatorics Geometry Algebraic Geometry Group Theory and Generalizations Mathematik Verallgemeinertes Polygon Gebäude Mathematik |
| url | https://doi.org/10.1007/978-3-662-04689-0 |
| work_keys_str_mv | AT titsjacques moufangpolygons AT weissrichardm moufangpolygons |