Grassmannians of classical buildings:
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore
World Scientific
©2010
|
| Series: | Algebra and discrete mathematics (World Scientific (Firm))
v. 2 |
| Subjects: | |
| Online Access: | FAW01 FAW02 Volltext |
| Item Description: | Includes bibliographical references (pages 207-210) and index 1. Linear algebra and projective geometry. 1.1. Vector spaces. 1.2. Projective spaces. 1.3. Semilinear mappings. 1.4. Fundamental theorem of projective geometry. 1.5. Reflexive forms and polarities -- 2. Buildings and Grassmannians. 2.1. Simplicial complexes. 2.2. Coxeter systems and Coxeter complexes. 2.3. Buildings. 2.4. Mappings of Grassmannians -- 3. Classical Grassmannians. 3.1. Elementary properties of Grassmann spaces. 3.2. Collineations of Grassmann spaces. 3.3. Apartments. 3.4. Apartments preserving mappings. 3.5. Grassmannians of exchange spaces. 3.6. Matrix geometry and spine spaces. 3.7. Geometry of linear involutions. 3.8. Grassmannians of infinite-dimensional vector spaces -- 4. Polar and half-spin Grassmannians. 4.1. Polar spaces. 4.2. Grassmannians. 4.3. Examples. 4.4. Polar buildings. 4.5. Elementary properties of Grassmann spaces. 4.6. Collineations. 4.7. Opposite relation. 4.8. Apartments. 4.9. Apartments preserving mappings Buildings are combinatorial constructions successfully exploited to study groups of various types. The vertex set of a building can be naturally decomposed into subsets called Grassmannians. The book contains both classical and more recent results on Grassmannians of buildings of classical types. It gives a modern interpretation of some classical results from the geometry of linear groups. The presented methods are applied to some geometric constructions non-related to buildings - Grassmannians of infinite-dimensional vector spaces and the sets of conjugate linear involutions. The book is self-contained and the requirement for the reader is a knowledge of basic algebra and graph theory. This makes it very suitable for use in a course for graduate students |
| Physical Description: | 1 Online-Ressource (xii, 212 pages) |
| ISBN: | 9789814317566 9789814317573 981431756X 9814317578 |
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| 500 | |a Buildings are combinatorial constructions successfully exploited to study groups of various types. The vertex set of a building can be naturally decomposed into subsets called Grassmannians. The book contains both classical and more recent results on Grassmannians of buildings of classical types. It gives a modern interpretation of some classical results from the geometry of linear groups. The presented methods are applied to some geometric constructions non-related to buildings - Grassmannians of infinite-dimensional vector spaces and the sets of conjugate linear involutions. The book is self-contained and the requirement for the reader is a knowledge of basic algebra and graph theory. This makes it very suitable for use in a course for graduate students | ||
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Record in the Search Index
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|---|---|
| any_adam_object | |
| author | Pankov, Mark |
| author_facet | Pankov, Mark |
| author_role | aut |
| author_sort | Pankov, Mark |
| author_variant | m p mp |
| building | Verbundindex |
| bvnumber | BV043170052 |
| collection | ZDB-4-EBA |
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| dewey-full | 514.34 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043170052 |
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| indexdate | 2024-07-10T07:19:38Z |
| institution | BVB |
| isbn | 9789814317566 9789814317573 981431756X 9814317578 |
| language | English |
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| spelling | Pankov, Mark Verfasser aut Grassmannians of classical buildings Mark Pankov Singapore World Scientific ©2010 1 Online-Ressource (xii, 212 pages) txt rdacontent c rdamedia cr rdacarrier Algebra and discrete mathematics (World Scientific (Firm)) v. 2 Includes bibliographical references (pages 207-210) and index 1. Linear algebra and projective geometry. 1.1. Vector spaces. 1.2. Projective spaces. 1.3. Semilinear mappings. 1.4. Fundamental theorem of projective geometry. 1.5. Reflexive forms and polarities -- 2. Buildings and Grassmannians. 2.1. Simplicial complexes. 2.2. Coxeter systems and Coxeter complexes. 2.3. Buildings. 2.4. Mappings of Grassmannians -- 3. Classical Grassmannians. 3.1. Elementary properties of Grassmann spaces. 3.2. Collineations of Grassmann spaces. 3.3. Apartments. 3.4. Apartments preserving mappings. 3.5. Grassmannians of exchange spaces. 3.6. Matrix geometry and spine spaces. 3.7. Geometry of linear involutions. 3.8. Grassmannians of infinite-dimensional vector spaces -- 4. Polar and half-spin Grassmannians. 4.1. Polar spaces. 4.2. Grassmannians. 4.3. Examples. 4.4. Polar buildings. 4.5. Elementary properties of Grassmann spaces. 4.6. Collineations. 4.7. Opposite relation. 4.8. Apartments. 4.9. Apartments preserving mappings Buildings are combinatorial constructions successfully exploited to study groups of various types. The vertex set of a building can be naturally decomposed into subsets called Grassmannians. The book contains both classical and more recent results on Grassmannians of buildings of classical types. It gives a modern interpretation of some classical results from the geometry of linear groups. The presented methods are applied to some geometric constructions non-related to buildings - Grassmannians of infinite-dimensional vector spaces and the sets of conjugate linear involutions. The book is self-contained and the requirement for the reader is a knowledge of basic algebra and graph theory. This makes it very suitable for use in a course for graduate students Submanifolds Mathematics MATHEMATICS / Topology bisacsh Architektur Mathematik Grassmann manifolds Architecture Mathematics Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf Gebäude Mathematik (DE-588)4123258-6 gnd rswk-swf Graßmann-Mannigfaltigkeit (DE-588)4158085-0 gnd rswk-swf Graßmann-Mannigfaltigkeit (DE-588)4158085-0 s Gruppe Mathematik (DE-588)4022379-6 s Gebäude Mathematik (DE-588)4123258-6 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=374869 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pankov, Mark Grassmannians of classical buildings Submanifolds Mathematics MATHEMATICS / Topology bisacsh Architektur Mathematik Grassmann manifolds Architecture Mathematics Gruppe Mathematik (DE-588)4022379-6 gnd Gebäude Mathematik (DE-588)4123258-6 gnd Graßmann-Mannigfaltigkeit (DE-588)4158085-0 gnd |
| subject_GND | (DE-588)4022379-6 (DE-588)4123258-6 (DE-588)4158085-0 |
| title | Grassmannians of classical buildings |
| title_auth | Grassmannians of classical buildings |
| title_exact_search | Grassmannians of classical buildings |
| title_full | Grassmannians of classical buildings Mark Pankov |
| title_fullStr | Grassmannians of classical buildings Mark Pankov |
| title_full_unstemmed | Grassmannians of classical buildings Mark Pankov |
| title_short | Grassmannians of classical buildings |
| title_sort | grassmannians of classical buildings |
| topic | Submanifolds Mathematics MATHEMATICS / Topology bisacsh Architektur Mathematik Grassmann manifolds Architecture Mathematics Gruppe Mathematik (DE-588)4022379-6 gnd Gebäude Mathematik (DE-588)4123258-6 gnd Graßmann-Mannigfaltigkeit (DE-588)4158085-0 gnd |
| topic_facet | Submanifolds Mathematics MATHEMATICS / Topology Architektur Mathematik Grassmann manifolds Architecture Mathematics Gruppe Mathematik Gebäude Mathematik Graßmann-Mannigfaltigkeit |
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