04794nam 22010094a 450 991081384550332120200520144314.01-282-12946-597866121294691-4008-2694-210.1515/9781400826940(CKB)1000000000756300(EBL)445567(OCoLC)362799544(SSID)ssj0000230980(PQKBManifestationID)11175054(PQKBTitleCode)TC0000230980(PQKBWorkID)10197490(PQKB)10708509(DE-B1597)446487(OCoLC)979592495(DE-B1597)9781400826940(Au-PeEL)EBL445567(CaPaEBR)ebr10284147(CaONFJC)MIL212946(PPN)199244707(PPN)187951233(FR-PaCSA)88838044(MiAaPQ)EBC445567(EXLCZ)99100000000075630020050330d2006 uy 0engur|n|---|||||txtccrQuadrangular algebras /Richard M. WeissCourse BookPrinceton, N.J. Princeton University Pressc20061 online resource (146 p.)Mathematical notes ;46Princeton paperbacksDescription based upon print version of record.0-691-12460-4 Includes bibliographical references (p. [133]) and index. 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 -- IndexThis 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 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.Mathematical notes (Princeton University Press) ;46.Princeton paperbacks.Forms, QuadraticAlgebraAlgebra over a field.Algebraic group.Associative property.Axiom.Classical group.Clifford algebra.Commutator.Defective matrix.Division algebra.Fiber bundle.Geometry.Isotropic quadratic form.Jacques Tits.Jordan algebra.Moufang.Non-associative algebra.Polygon.Precalculus.Projective plane.Quadratic form.Simple Lie group.Subgroup.Theorem.Vector space.Forms, Quadratic.Algebra.512.7/431.20bclWeiss Richard M(Richard Mark),1946-1598284MiAaPQMiAaPQMiAaPQBOOK9910813845503321Quadrangular algebras3920424UNINA