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Grassmannians of classical buildings /

Pankov, Mark.

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Grassmannians of classical buildings /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Grassmannians of classical buildings // Mark Pankov.
Author:	Pankov, Mark.
Published:	Singapore ;World Scientific, : c2010.,
Description:	xii, 212 p. :ill. ;24 cm.
Subject:	Grassmann manifolds. -
ISBN:	9789814317566

Grassmannians of classical buildings /
Pankov, Mark.

Grassmannians of classical buildings /Mark Pankov. - Singapore ;World Scientific,c2010. - xii, 212 p. :ill. ;24 cm. - Algebra and discrete mathematics,v. 21793-5873 ;. - Algebra and discrete mathematics (World Scientific (Firm)) ;v. 2..

Includes bibliographical references (p. 207-210) and index.

Vector spaces --Machine generated contents note:

ISBN: 9789814317566

LCCN: 2012405646Subjects--Topical Terms:

708971
Grassmann manifolds.

LC Class. No.: QA613.6 / .P36 2010

Dewey Class. No.: 514.34

Grassmannians of classical buildings /
LDR:04803cam a22002657a 4500 001 2439908
005 20250607051248.9
008 261021s2010 si a b 001 0 eng
010 $a 2012405646
020 $a 9789814317566 $q hbk.
020 $a 981431756X $q hbk.
035 $a 17393560
035 $a (OCoLC)613430940
040 $a UKM $c UKM $d BTCTA $d YDXCP $d C#P $d BWX $d COD $d INU $d DLC
042 $a lccopycat
050 0 0 $a QA613.6 $b .P36 2010
082 0 4 $a 514.34 $2 22
100 1 $a Pankov, Mark. $3 3831722
245 1 0 $a Grassmannians of classical buildings / $c Mark Pankov.
260 # $a Singapore ; $a Hackensack, NJ : $b World Scientific, $c c2010.
300 $a xii, 212 p. : $b ill. ; $c 24 cm.
490 1 $a Algebra and discrete mathematics, $x 1793-5873 ; $v v. 2
504 $a Includes bibliographical references (p. 207-210) and index.
505 0 0 $g Machine generated contents note: $g 1.1. $t Vector spaces -- $g 1.1.1. $t Division rings -- $g 1.1.2. $t Vector spaces over division rings -- $g 1.1.3. $t Dual vector space -- $g 1.2. $t Projective spaces -- $g 1.2.1. $t Linear and partial linear spaces -- $g 1.2.2. $t Projective spaces over division rings -- $g 1.3. $t Semilinear mappings -- $g 1.3.1. $t Definitions -- $g 1.3.2. $t Mappings of Grassmannians induced by semilinear mappings -- $g 1.3.3. $t Contragradient -- $g 1.4. $t Fundamental Theorem of Projective Geometry -- $g 1.4.1. $t Main theorem and corollaries -- $g 1.4.2. $t Proof of Theorem 1.4 -- $g 1.4.3. $t Fundamental Theorem for normed spaces -- $g 1.4.4. $t Proof of Theorem 1.5 -- $g 1.5. $t Reflexive forms and polarities -- $g 1.5.1. $t Sesquilinear forms -- $g 1.5.2. $t Reflexive forms -- $g 1.5.3. $t Polarities -- $g 2.1. $t Simplicial complexes -- $g 2.1.1. $t Definition and examples -- $g 2.1.2. $t Chamber complexes -- $g 2.1.3. $t Grassmannians and Grassmann spaces -- $g 2.2. $t Coxeter systems and Coxeter complexes
505 0 0 $g 2.2.1. $t Coxeter systems -- $g 2.2.2. $t Coxeter complexes -- $g 2.2.3. $t Three examples -- $g 2.3. $t Buildings -- $g 2.3.1. $t Definition and elementary properties -- $g 2.3.2. $t Buildings and Tits systems -- $g 2.3.3. $t Classical examples -- $g 2.3.4. $t Spherical buildings -- $g 2.3.5. $t Mappings of the chamber sets -- $g 2.4. $t Mappings of Grassmannians -- $g 2.5. $t Appendix: Gamma spaces -- $g 3.1. $t Elementary properties of Grassmann spaces -- $g 3.2. $t Collineations of Grassmann spaces -- $g 3.2.1. $t Chow's theorem -- $g 3.2.2. $t Chow's theorem for linear spaces -- $g 3.2.3. $t Applications of Chow's theorem -- $g 3.2.4. $t Opposite relation -- $g 3.3. $t Apartments -- $g 3.3.1. $t Basic properties -- $g 3.3.2. $t Proof of Theorem 3.8 -- $g 3.4. $t Apartments preserving mappings -- $g 3.4.1. $t Results -- $g 3.4.2. $t Proof of Theorem 3.10: First step -- $g 3.4.3. $t Proof of Theorem 3.10: Second step -- $g 3.5. $t Grassmannians of exchange spaces -- $g 3.5.1. $t Exchange spaces -- $g 3.5.2. $t Grassmannians -- $g 3.6. $t Matrix geometry and spine spaces -- $g 3.7. $t Geometry of linear involutions
505 0 0 $g 3.7.1. $t Involutions and transvections -- $g 3.7.2. $t Adjacency relation -- $g 3.7.3. $t Chow's theorem for linear involutions -- $g 3.7.4. $t Proof of Theorem 3.15 -- $g 3.7.5. $t Automorphisms of the group GL(V) -- $g 3.8. $t Grassmannians of infinite-dimensional vector spaces -- $g 3.8.1. $t Adjacency relation -- $g 3.8.2. $t Proof of Theorem 3.17 -- $g 3.8.3. $t Base subsets -- $g 3.8.4. $t Proof of Theorem 3.18 -- $g 4.1. $t Polar spaces -- $g 4.1.1. $t Axioms and elementary properties -- $g 4.1.2. $t Proof of Theorem 4.1 -- $g 4.1.3. $t Corollaries of Theorem 4.1 -- $g 4.1.4. $t Polar frames -- $g 4.2. $t Grassmannians -- $g 4.2.1. $t Polar Grassmannians -- $g 4.2.2. $t Two types of polar spaces -- $g 4.2.3. $t Half-spin Grassmannians -- $g 4.3. $t Examples -- $g 4.3.1. $t Polar spaces associated with sesquilinear forms -- $g 4.3.2. $t Polar spaces associated with quadratic forms -- $g 4.3.3. $t Polar spaces of type D3 -- $g 4.3.4. $t Embeddings in projective spaces and classification -- $g 4.4. $t Polar buildings -- $g 4.4.1. $t Buildings of type Cn -- $g 4.4.2. $t Buildings of type Dn -- $g 4.5. $t Elementary properties of Grassmann spaces
505 0 0 $g 4.5.1. $t Polar Grassmann spaces -- $g 4.5.2. $t Half-spin Grassmann spaces -- $g 4.6. $t Collineations -- $g 4.6.1. $t Chow's theorem and its generalizations -- $g 4.6.2. $t Weak adjacency on polar Grassmannians -- $g 4.6.3. $t Proof of Theorem 4.8 for k < n [ -- ] 2 -- $g 4.6.4. $t Proof of Theorems 4.7 and -- $g 4.6.5. $t Proof of Theorem 4.9 -- $g 4.6.6. $t Remarks -- $g 4.7. $t Opposite relation -- $g 4.7.1. $t Opposite relation on polar Grassmannians -- $g 4.7.2. $t Opposite relation on half-spin Grassmannians -- $g 4.8. $t Apartments -- $g 4.8.1. $t Apartments in polar Grassmannians -- $g 4.8.2. $t Apartments in half-spin Grassmannians -- $g 4.8.3. $t Proof of Theorem 4.15 -- $g 4.9. $t Apartments preserving mappings -- $g 4.9.1. $t Apartments preserving bijections -- $g 4.9.2. $t Inexact subsets of polar Grassmannians -- $g 4.9.3. $t Complement subsets of polar Grassmannians -- $g 4.9.4. $t Inexact subsets of half-spin Grassmannians -- $g 4.9.5. $t Proof of Theorem 4.16 -- $g 4.9.6. $t Embeddings -- $g 4.9.7. $t Proof of Theorems 4.17 and 4.18.
650 # 0 $a Grassmann manifolds. $3 708971
650 # 0 $a Architecture $x Mathematics. $3 863055
830 0 $a Algebra and discrete mathematics (World Scientific (Firm)) ; $v v. 2. $3 3831723