Grassmannians of classical buildings /
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| Author / Creator: | Pankov, Mark. |
|---|---|
| Imprint: | Singapore ; Hackensack, NJ : World Scientific, ©2010. |
| Description: | 1 online resource (xii, 212 pages) : illustrations |
| Language: | English |
| Series: | Algebra and discrete mathematics, 1793-5873 ; v. 2 Algebra and discrete mathematics (World Scientific (Firm)) ; v. 2. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11258664 |
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| 100 | 1 | |a Pankov, Mark. | |
| 245 | 1 | 0 | |a Grassmannians of classical buildings / |c Mark Pankov. |
| 260 | |a Singapore ; |a Hackensack, NJ : |b World Scientific, |c ©2010. | ||
| 300 | |a 1 online resource (xii, 212 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
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| 490 | 1 | |a Algebra and discrete mathematics, |x 1793-5873 ; |v v. 2 | |
| 504 | |a Includes bibliographical references (pages 207-210) and index. | ||
| 505 | 0 | |a 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. | |
| 520 | |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. | ||
| 588 | 0 | |a Print version record. | |
| 546 | |a English. | ||
| 650 | 0 | |a Grassmann manifolds. |0 http://id.loc.gov/authorities/subjects/sh85056534 | |
| 650 | 0 | |a Architecture |x Mathematics. |0 http://id.loc.gov/authorities/subjects/sh2009001569 | |
| 650 | 7 | |a MATHEMATICS |x Topology. |2 bisacsh | |
| 650 | 7 | |a Architecture |x Mathematics. |2 fast |0 (OCoLC)fst00813479 | |
| 650 | 7 | |a Grassmann manifolds. |2 fast |0 (OCoLC)fst00946825 | |
| 655 | 0 | |a Electronic books. | |
| 655 | 4 | |a Electronic books. | |
| 776 | 0 | 8 | |i Print version: |a Pankov, Mark. |t Grassmannians of classical buildings. |d Singapore ; Hackensack, NJ : World Scientific, ©2010 |z 9789814317566 |w (OCoLC)613430940 |
| 830 | 0 | |a Algebra and discrete mathematics (World Scientific (Firm)) ; |v v. 2. |0 http://id.loc.gov/authorities/names/no2009082509 | |
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| 928 | |t Library of Congress classification |a QA613.2 .P36 2010eb |l Online |c UC-FullText |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=e000xna&AN=374869 |z eBooks on EBSCOhost |g ebooks |i 12351566 | ||