Moufang polygons /
"This book gives the complete classification of Moufang polygons. It also contains a new proof of the classification of irreducible spherical buildings of rank at least three based on the observation that all the irreducible rank two residues of such a building are Moufang polygons. In an appen...
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| Other Authors: | , |
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; New York :
Springer,
[2002], ©2002
Berlin ; New York : c2002 Berlin ; New York : ©2002 New York : 2002 Berlin ; New York : 2002 |
| Series: | Springer monographs in mathematics
Springer monographs in mathematics, Springer monographs in mathematics Springer monographs in mathematics |
| Subjects: |
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| 100 | 1 | |a Tits, Jacques |1 http://viaf.org/viaf/41847224 | |
| 100 | 1 | |a Tits, Jacques | |
| 245 | 1 | 0 | |a Moufang polygons / |c Jacques Tits, Richard M. Weiss |
| 260 | |a Berlin ; |a New York : |b Springer, |c [2002], ©2002 | ||
| 260 | |a Berlin ; |a New York : |b Springer, |c c2002 | ||
| 260 | |a Berlin ; |a New York : |b Springer, |c ©2002 | ||
| 260 | |a New York : |b Springer, |c 2002 | ||
| 264 | 1 | |a Berlin ; |a New York : |b Springer, |c 2002 | |
| 300 | |a ix, 535 p. : |b ill. ; |c 24 cm | ||
| 300 | |a ix, 535 pages : |b illustrations ; |c 24 cm | ||
| 300 | |a ix, 535 pages : |b illustrations ; |c 25 cm | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 440 | 0 | |a Springer monographs in mathematics |x 1439-7382 | |
| 440 | 0 | |a Springer monographs in mathematics, |x 1439-7382 | |
| 490 | 1 | |a Springer monographs in mathematics, |x 1439-7382 | |
| 500 | |a This WorldCat-derived record is shareable under Open Data Commons ODC-BY, with attribution to OCLC |5 CTY | ||
| 504 | |a Includes bibliographical references (p. [521]-526) and indexes | ||
| 504 | |a Includes bibliographical references (pages [521]-526) and index | ||
| 504 | |a Includes bibliographical references (pages [521]-526) and indexes | ||
| 504 | |a Includes bibliographical references and index | ||
| 505 | 0 | 0 | |g Pt. I |t Preliminary Results -- |g 1. |t Introduction -- |g 2. |t Some Definitions -- |g 3. |t Generalized Polygons -- |g 4. |t Moufang Polygons -- |g 5. |t Commutator Relations -- |g 6. |t Opposite Root Groups -- |g 7. |t A Uniqueness Lemma -- |g 8. |t A Construction -- |g Pt. II. |t Nine Families of Moufang Polygons -- |g 9. |t Alternative Division Rings, I -- |g 10. |t Indifferent and Octagonal Sets -- |g 11. |t Involutory Sets and Pseudo-Quadratic Forms -- |g 12. |t Quadratic Forms of Type E[subscript 6], E[subscript 7] and E[subscript 8], I -- |g 13. |t Quadratic Forms of Type E[subscript 6], E[subscript 7] and E[subscript 8], II -- |g 14. |t Quadratic Forms of Type F[subscript 4] -- |g 15. |t Hexagonal Systems, I -- |g 16. |t An Inventory of Moufang Polygons -- |g 17. |t Main Results -- |g Pt. III. |t The Classification of Moufang Polygons -- |g 18. |t A Bound on n -- |g 19. |t Triangles -- |g 20. |t Alternative Division Rings, II -- |g 21. |t Quadrangles -- |g 22. |t Quadrangles of Involution Type -- |g 23. |t Quadrangles of Quadratic Form Type -- |g 24. |t Quadrangles of Indifferent Type -- |g 25. |t Quadrangles of Pseudo-Quadratic Form Type, I -- |g 26. |t Quadrangles of Pseudo-Quadratic Form Type, II -- |g 27. |t Quadrangles of Type E[subscript 6], E[subscript 7] and E[subscript 8] -- |g 28. |t Quadrangles of Type F[subscript 4] -- |g 29. |t Hexagons -- |g 30. |t Hexagonal Systems, II -- |g 31. |t Octagons -- |g 32. |t Existence -- |g Pt. IV. |t More Results on Moufang Polygons -- |g 33. |t BN-Pairs -- |g 34. |t Finite Moufang Polygons -- |g 35. |t Isotopes -- |g 36. |t Isomorphic Hexagonal Systems -- |g 37. |t Automorphisms -- |g 38. |t Isomorphic Quadrangles -- |g Pt. V. |t Moufang Polygons and Spherical Buildings -- |g 39. |t Chamber Systems -- |g 40. |t Spherical Buildings -- |g 41. |t Classical, Algebraic and Mixed Buildings -- |g 42. |t Appendix. |
| 505 | 0 | 0 | |g Pt. I |t Preliminary Results. |g 1. |t Introduction. |g 2. |t Some Definitions. |g 3. |t Generalized Polygons. |g 4. |t Moufang Polygons. |g 5. |t Commutator Relations. |g 6. |t Opposite Root Groups. |g 7. |t A Uniqueness Lemma. |g 8. |t A Construction -- |g Pt. II. |t Nine Families of Moufang Polygons. |g 9. |t Alternative Division Rings, I. |g 10. |t Indifferent and Octagonal Sets. |g 11. |t Involutory Sets and Pseudo-Quadratic Forms. |g 12. |t Quadratic Forms of Type E[subscript 6], E[subscript 7] and E[subscript 8], I. |g 13. |t Quadratic Forms of Type E[subscript 6], E[subscript 7] and E[subscript 8], II. |g 14. |t Quadratic Forms of Type F[subscript 4]. |g 15. |t Hexagonal Systems, I. |g 16. |t An Inventory of Moufang Polygons. |g 17. |t Main Results -- |g Pt. III. |t The Classification of Moufang Polygons. |g 18. |t A Bound on n. |
| 520 | 1 | |a "This book gives the complete classification of Moufang polygons. It also contains a new proof of the classification of irreducible spherical buildings of rank at least three based on the observation that all the irreducible rank two residues of such a building are Moufang polygons. In an appendix, the connection between spherical buildings and algebraic groups is recalled and used to describe an alternative existence proof for the exceptional Moufang polygons."--BOOK JACKET | |
| 596 | |a 4 | ||
| 650 | 0 | |a Buildings (Group theory) | |
| 650 | 0 | |a Graph theory | |
| 650 | 0 | |a Moufang loops | |
| 650 | 7 | |a Buildings (Group theory) |2 fast | |
| 650 | 7 | |a Graph theory |2 fast | |
| 650 | 7 | |a Moufang loops |2 fast | |
| 700 | 1 | |a Weiss, Richard M |q (Richard Mark), |d 1946- | |
| 700 | 1 | |a Weiss, Richard M | |
| 776 | 1 | |w (OCoLC)851383511 | |
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| 830 | 0 | |a Springer monographs in mathematics | |
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