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1. |
Record Nr. |
UNINA9910777726303321 |
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Autore |
Weiss Richard M (Richard Mark), <1946-> |
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Titolo |
Quadrangular algebras [[electronic resource] /] / Richard M. Weiss |
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Pubbl/distr/stampa |
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Princeton, N.J., : Princeton University Press, c2006 |
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ISBN |
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1-282-12946-5 |
9786612129469 |
1-4008-2694-2 |
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Edizione |
[Course Book] |
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Descrizione fisica |
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1 online resource (146 p.) |
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Collana |
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Mathematical notes ; ; 46 |
Princeton paperbacks |
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Classificazione |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. [133]) and index. |
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Nota di contenuto |
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Frontmatter -- Contents -- Preface -- Chapter One. Basic Definitions -- Chapter Two. Quadratic Forms -- Chapter Three. Quadrangular Algebras -- Chapter Four. Proper Quadrangular Algebras -- Chapter Five. Special Quadrangular Algebras -- Chapter Six. Regular Quadrangular Algebras -- Chapter Seven. Defective Quadrangular Algebras -- Chapter Eight. Isotopes -- Chapter Nine. Improper Quadrangular Algebras -- Chapter Ten. Existence -- Chapter Eleven. Moufang Quadrangles -- Chapter Twelve. The Structure Group -- Bibliography -- Index |
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Sommario/riassunto |
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This book introduces a new class of non-associative algebras related to certain exceptional algebraic groups and their associated buildings. Richard Weiss develops a theory of these "quadrangular algebras" that opens the first purely algebraic approach to the exceptional Moufang quadrangles. These quadrangles include both those that arise as the spherical buildings associated to groups of type E6, E7, and E8 as well as the exotic quadrangles "of type F4" discovered earlier by Weiss. Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras. Formally, the notion of a quadrangular algebra is derived from the notion of a pseudo-quadratic space (introduced by |
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Jacques Tits in the study of classical groups) over a quaternion division ring. This book contains the complete classification of quadrangular algebras starting from first principles. It also shows how this classification can be made to yield the classification of exceptional Moufang quadrangles as a consequence. The book closes with a chapter on isotopes and the structure group of a quadrangular algebra. Quadrangular Algebras is intended for graduate students of mathematics as well as specialists in buildings, exceptional algebraic groups, and related algebraic structures including Jordan algebras and the algebraic theory of quadratic forms. |
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2. |
Record Nr. |
UNINA9910154749003321 |
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Autore |
Madsen Ib |
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Titolo |
Classifying Spaces for Surgery and Corbordism of Manifolds. (AM-92), Volume 92 / / R. James Milgram, Ib Madsen |
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Pubbl/distr/stampa |
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Princeton, NJ : , : Princeton University Press, , [2016] |
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©1980 |
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ISBN |
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Descrizione fisica |
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1 online resource (296 pages) : illustrations |
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Collana |
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Annals of Mathematics Studies ; ; 229 |
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Disciplina |
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Soggetti |
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Manifolds (Mathematics) |
Classifying spaces |
Surgery (Topology) |
Cobordism theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Frontmatter -- CONTENTS -- INTRODUCTION -- CHAPTER 1. CLASSIFYING SPACES AND COBORDISM -- CHAPTER 2. THE SURGERY CLASSIFICATION OF MANIFOLDS -- CHAPTER 3. THE SPACES SG AND BSG -- CHAPTER 4. THE HOMOTOPY STRUCTURE OF G/PL AND G/TOP -- CHAPTER 5. THE HOMOTOPY STRUCTURE OF MSPL[½] AND MSTOP[½] -- CHAPTER 6 . INFINITE LOOP SPACES AND THEIR HOMOLOGY OPERATIONS -- CHAPTER 7. THE 2-LOCAL STRUCTURE OF B(G/TOP) -- |
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CHAPTER 8 . THE TORSION FREE STRUCTURE OF THE ORIENTED COBORDISM RINGS -- CHAPTER 9. THE TORSION FREE COHOMOLOGY OF G/TOP AND G/PL -- CHAPTER 10. THE TORSION FREE COHOMOLOGY OF BTOP AND BPL -- CHAPTER 11. INTEGRALITY THEOREMS -- CHAPTER 12. THE SMOOTH SURGERY CLASSES AND H*(BTOP; ℤ/2) -- CHAPTER 13. THE BOCKSTEIN SPECTRAL SEQUENCE FOR BTOP -- CHAPTER 14. THE TYPES OF TORSION GENERATORS -- APPENDIX. THE PROOFS OF 13.12, 13.13, AND 13.15 -- BIBLIOGRAPHY -- INDEX -- Backmatter |
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Sommario/riassunto |
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Beginning with a general discussion of bordism, Professors Madsen and Milgram present the homotopy theory of the surgery classifying spaces and the classifying spaces for the various required bundle theories. The next part covers more recent work on the maps between these spaces and the properties of the PL and Top characteristic classes, and includes integrality theorems for topological and PL manifolds. Later chapters treat the integral cohomology of BPL and Btop. The authors conclude with a discussion of the PL and topological cobordism rings and a construction of the torsion-free generators. |
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