Grassmannians of classical buildings /

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Bibliographic Details
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:	Grassmann manifolds. Architecture -- Mathematics. Architecture -- Mathematics. Grassmann manifolds. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11258664

Hidden Bibliographic Details
ISBN:	9789814317573 9814317578 1283144867 9781283144865 9789814317566 981431756X 9786613144867 661314486X
Digital file characteristics:	data file
Notes:	Includes bibliographical references (pages 207-210) and index. English. Print version record.
Summary:	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.
Other form:	Print version: Pankov, Mark. Grassmannians of classical buildings. Singapore ; Hackensack, NJ : World Scientific, ©2010 9789814317566

Table of Contents:

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.

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