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• 2012405646 contributor B12575882.
• 2012405646 created "c2010.".
• 2012405646 date "2010".
• 2012405646 date "c2010.".
• 2012405646 dateCopyrighted "c2010.".
• 2012405646 description "2.2.1. Coxeter systems -- 2.2.2. Coxeter complexes -- 2.2.3. Three examples -- 2.3. Buildings -- 2.3.1. Definition and elementary properties -- 2.3.2. Buildings and Tits systems -- 2.3.3. Classical examples -- 2.3.4. Spherical buildings -- 2.3.5. Mappings of the chamber sets -- 2.4. Mappings of Grassmannians -- 2.5. Appendix: Gamma spaces -- 3.1. Elementary properties of Grassmann spaces -- 3.2. Collineations of Grassmann spaces -- 3.2.1. Chow's theorem -- 3.2.2. Chow's theorem for linear spaces -- 3.2.3. Applications of Chow's theorem -- 3.2.4. Opposite relation -- 3.3. Apartments -- 3.3.1. Basic properties -- 3.3.2. Proof of Theorem 3.8 -- 3.4. Apartments preserving mappings -- 3.4.1. Results -- 3.4.2. Proof of Theorem 3.10: First step -- 3.4.3. Proof of Theorem 3.10: Second step -- 3.5. Grassmannians of exchange spaces -- 3.5.1. Exchange spaces -- 3.5.2. Grassmannians -- 3.6. Matrix geometry and spine spaces -- 3.7. Geometry of linear involutions".
• 2012405646 description "3.7.1. Involutions and transvections -- 3.7.2. Adjacency relation -- 3.7.3. Chow's theorem for linear involutions -- 3.7.4. Proof of Theorem 3.15 -- 3.7.5. Automorphisms of the group GL(V) -- 3.8. Grassmannians of infinite-dimensional vector spaces -- 3.8.1. Adjacency relation -- 3.8.2. Proof of Theorem 3.17 -- 3.8.3. Base subsets -- 3.8.4. Proof of Theorem 3.18 -- 4.1. Polar spaces -- 4.1.1. Axioms and elementary properties -- 4.1.2. Proof of Theorem 4.1 -- 4.1.3. Corollaries of Theorem 4.1 -- 4.1.4. Polar frames -- 4.2. Grassmannians -- 4.2.1. Polar Grassmannians -- 4.2.2. Two types of polar spaces -- 4.2.3. Half-spin Grassmannians -- 4.3. Examples -- 4.3.1. Polar spaces associated with sesquilinear forms -- 4.3.2. Polar spaces associated with quadratic forms -- 4.3.3. Polar spaces of type D3 -- 4.3.4. Embeddings in projective spaces and classification -- 4.4. Polar buildings -- 4.4.1. Buildings of type Cn -- 4.4.2. Buildings of type Dn -- 4.5. Elementary properties of Grassmann spaces".
• 2012405646 description "4.5.1. Polar Grassmann spaces -- 4.5.2. Half-spin Grassmann spaces -- 4.6. Collineations -- 4.6.1. Chow's theorem and its generalizations -- 4.6.2. Weak adjacency on polar Grassmannians -- 4.6.3. Proof of Theorem 4.8 for k < n [ -- ] 2 -- 4.6.4. Proof of Theorems 4.7 and -- 4.6.5. Proof of Theorem 4.9 -- 4.6.6. Remarks -- 4.7. Opposite relation -- 4.7.1. Opposite relation on polar Grassmannians -- 4.7.2. Opposite relation on half-spin Grassmannians -- 4.8. Apartments -- 4.8.1. Apartments in polar Grassmannians -- 4.8.2. Apartments in half-spin Grassmannians -- 4.8.3. Proof of Theorem 4.15 -- 4.9. Apartments preserving mappings -- 4.9.1. Apartments preserving bijections -- 4.9.2. Inexact subsets of polar Grassmannians -- 4.9.3. Complement subsets of polar Grassmannians -- 4.9.4. Inexact subsets of half-spin Grassmannians -- 4.9.5. Proof of Theorem 4.16 -- 4.9.6. Embeddings -- 4.9.7. Proof of Theorems 4.17 and 4.18.".
• 2012405646 description "Includes bibliographical references (p. 207-210) and index.".
• 2012405646 description "Machine generated contents note: 1.1. Vector spaces -- 1.1.1. Division rings -- 1.1.2. Vector spaces over division rings -- 1.1.3. Dual vector space -- 1.2. Projective spaces -- 1.2.1. Linear and partial linear spaces -- 1.2.2. Projective spaces over division rings -- 1.3. Semilinear mappings -- 1.3.1. Definitions -- 1.3.2. Mappings of Grassmannians induced by semilinear mappings -- 1.3.3. Contragradient -- 1.4. Fundamental Theorem of Projective Geometry -- 1.4.1. Main theorem and corollaries -- 1.4.2. Proof of Theorem 1.4 -- 1.4.3. Fundamental Theorem for normed spaces -- 1.4.4. Proof of Theorem 1.5 -- 1.5. Reflexive forms and polarities -- 1.5.1. Sesquilinear forms -- 1.5.2. Reflexive forms -- 1.5.3. Polarities -- 2.1. Simplicial complexes -- 2.1.1. Definition and examples -- 2.1.2. Chamber complexes -- 2.1.3. Grassmannians and Grassmann spaces -- 2.2. Coxeter systems and Coxeter complexes".
• 2012405646 extent "xii, 212 p. :".
• 2012405646 identifier "9789814317566 (hbk.)".
• 2012405646 identifier "981431756X (hbk.)".
• 2012405646 isPartOf "Algebra and discrete mathematics (World Scientific (Firm)) ; v. 2.".
• 2012405646 isPartOf "Algebra and discrete mathematics, 1793-5873 ; v. 2".
• 2012405646 issued "2010".
• 2012405646 issued "c2010.".
• 2012405646 language "eng".
• 2012405646 publisher "Singapore ; Hackensack, NJ : World Scientific,".
• 2012405646 subject "514.34 22".
• 2012405646 subject "Architecture Mathematics.".
• 2012405646 subject "Grassmann manifolds.".
• 2012405646 subject "QA613.6 .P36 2010".
• 2012405646 tableOfContents "2.2.1. Coxeter systems -- 2.2.2. Coxeter complexes -- 2.2.3. Three examples -- 2.3. Buildings -- 2.3.1. Definition and elementary properties -- 2.3.2. Buildings and Tits systems -- 2.3.3. Classical examples -- 2.3.4. Spherical buildings -- 2.3.5. Mappings of the chamber sets -- 2.4. Mappings of Grassmannians -- 2.5. Appendix: Gamma spaces -- 3.1. Elementary properties of Grassmann spaces -- 3.2. Collineations of Grassmann spaces -- 3.2.1. Chow's theorem -- 3.2.2. Chow's theorem for linear spaces -- 3.2.3. Applications of Chow's theorem -- 3.2.4. Opposite relation -- 3.3. Apartments -- 3.3.1. Basic properties -- 3.3.2. Proof of Theorem 3.8 -- 3.4. Apartments preserving mappings -- 3.4.1. Results -- 3.4.2. Proof of Theorem 3.10: First step -- 3.4.3. Proof of Theorem 3.10: Second step -- 3.5. Grassmannians of exchange spaces -- 3.5.1. Exchange spaces -- 3.5.2. Grassmannians -- 3.6. Matrix geometry and spine spaces -- 3.7. Geometry of linear involutions".
• 2012405646 tableOfContents "3.7.1. Involutions and transvections -- 3.7.2. Adjacency relation -- 3.7.3. Chow's theorem for linear involutions -- 3.7.4. Proof of Theorem 3.15 -- 3.7.5. Automorphisms of the group GL(V) -- 3.8. Grassmannians of infinite-dimensional vector spaces -- 3.8.1. Adjacency relation -- 3.8.2. Proof of Theorem 3.17 -- 3.8.3. Base subsets -- 3.8.4. Proof of Theorem 3.18 -- 4.1. Polar spaces -- 4.1.1. Axioms and elementary properties -- 4.1.2. Proof of Theorem 4.1 -- 4.1.3. Corollaries of Theorem 4.1 -- 4.1.4. Polar frames -- 4.2. Grassmannians -- 4.2.1. Polar Grassmannians -- 4.2.2. Two types of polar spaces -- 4.2.3. Half-spin Grassmannians -- 4.3. Examples -- 4.3.1. Polar spaces associated with sesquilinear forms -- 4.3.2. Polar spaces associated with quadratic forms -- 4.3.3. Polar spaces of type D3 -- 4.3.4. Embeddings in projective spaces and classification -- 4.4. Polar buildings -- 4.4.1. Buildings of type Cn -- 4.4.2. Buildings of type Dn -- 4.5. Elementary properties of Grassmann spaces".
• 2012405646 tableOfContents "4.5.1. Polar Grassmann spaces -- 4.5.2. Half-spin Grassmann spaces -- 4.6. Collineations -- 4.6.1. Chow's theorem and its generalizations -- 4.6.2. Weak adjacency on polar Grassmannians -- 4.6.3. Proof of Theorem 4.8 for k < n [ -- ] 2 -- 4.6.4. Proof of Theorems 4.7 and -- 4.6.5. Proof of Theorem 4.9 -- 4.6.6. Remarks -- 4.7. Opposite relation -- 4.7.1. Opposite relation on polar Grassmannians -- 4.7.2. Opposite relation on half-spin Grassmannians -- 4.8. Apartments -- 4.8.1. Apartments in polar Grassmannians -- 4.8.2. Apartments in half-spin Grassmannians -- 4.8.3. Proof of Theorem 4.15 -- 4.9. Apartments preserving mappings -- 4.9.1. Apartments preserving bijections -- 4.9.2. Inexact subsets of polar Grassmannians -- 4.9.3. Complement subsets of polar Grassmannians -- 4.9.4. Inexact subsets of half-spin Grassmannians -- 4.9.5. Proof of Theorem 4.16 -- 4.9.6. Embeddings -- 4.9.7. Proof of Theorems 4.17 and 4.18.".
• 2012405646 tableOfContents "Machine generated contents note: 1.1. Vector spaces -- 1.1.1. Division rings -- 1.1.2. Vector spaces over division rings -- 1.1.3. Dual vector space -- 1.2. Projective spaces -- 1.2.1. Linear and partial linear spaces -- 1.2.2. Projective spaces over division rings -- 1.3. Semilinear mappings -- 1.3.1. Definitions -- 1.3.2. Mappings of Grassmannians induced by semilinear mappings -- 1.3.3. Contragradient -- 1.4. Fundamental Theorem of Projective Geometry -- 1.4.1. Main theorem and corollaries -- 1.4.2. Proof of Theorem 1.4 -- 1.4.3. Fundamental Theorem for normed spaces -- 1.4.4. Proof of Theorem 1.5 -- 1.5. Reflexive forms and polarities -- 1.5.1. Sesquilinear forms -- 1.5.2. Reflexive forms -- 1.5.3. Polarities -- 2.1. Simplicial complexes -- 2.1.1. Definition and examples -- 2.1.2. Chamber complexes -- 2.1.3. Grassmannians and Grassmann spaces -- 2.2. Coxeter systems and Coxeter complexes".
• 2012405646 title "Grassmannians of classical buildings / Mark Pankov.".
• 2012405646 type "text".