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010 a| 2012405646;

015 a| GBB0907252| bnb;

016 7 a| 0156124622| Uk;

020 a| 9789814317566 (hbk.);

020 a| 981431756X (hbk.);

035 a| (WaSeSS)ssj0000636041;

042 a| lccopycat;

049 a| EREEa| NEHH;

050 00 a| QA613.6b| .P36 2010;

082 04 a| 514.342| 22;

100 1 a| Pankov, Mark.?| UNAUTHORIZED;

245 10 a| Grassmannians of classical buildingsh| [electronic resource] /c| Mark Pankov.;

260 a| Singapore ;a| Hackensack, NJ :b| World Scientific,;

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 00 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 00 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 00 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 00 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.;

506 a| Available only to authorized users.;

538 a| Mode of access: World Wide Web;

650 0 a| Grassmann manifolds.=| ^A97834;

650 0 a| Architecturex| Mathematics.=| ^A1304912;

655 0 a| Electronic books.=| ^A491897;

830 0 a| Algebra and discrete mathematics (World Scientific (Firm)) ;v| v. 2.=| ^A1255836;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=731314;

947 a| (OCoLC)ocn613430940;

949 a| CLICK ON WEB ADDRESSw| ASISh| JOYNER188;

949 a| CLICK ON WEB ADDRESSw| ASISh| HSL77;

949 a| CLICK ON WEB ADDRESSw| ASISh| JMUSIC60;

596 a| 1 3 4;

998 a| 6456889;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6456889-1001l| JNETm| JOYNERr| Ys| Yt| JNESSBKu| 7/20/2024x| EBOOKz| JERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6456889-2001l| HSLELECm| HSLr| Ys| Yt| HEBKu| 7/20/2024x| EBOOKz| HERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6456889-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 7/20/2024x| EBOOKz| JERESOURCE;

Grassmannians of classical buildings / Mark Pankov.

Author/creator	Pankov, Mark
Format	Electronic
Publication Info	Singapore ; Hackensack, NJ : World Scientific,
Description	xii, 212 p. : ill. ; 24 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Grassmann manifolds. Architecture--Mathematics.

Series	Algebra and discrete mathematics, 1793-5873 ; v. 2 Algebra and discrete mathematics (World Scientific (Firm)) ; v. 2. ^A1255836
Contents	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
Contents	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
Contents	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
Contents	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.
Bibliography note	Includes bibliographical references (p. 207-210) and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2012405646
ISBN	9789814317566 (hbk.)
ISBN	981431756X (hbk.)

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