LEADER 04794nam 22010094a 450 001 9910813845503321 005 20200520144314.0 010 $a1-282-12946-5 010 $a9786612129469 010 $a1-4008-2694-2 024 7 $a10.1515/9781400826940 035 $a(CKB)1000000000756300 035 $a(EBL)445567 035 $a(OCoLC)362799544 035 $a(SSID)ssj0000230980 035 $a(PQKBManifestationID)11175054 035 $a(PQKBTitleCode)TC0000230980 035 $a(PQKBWorkID)10197490 035 $a(PQKB)10708509 035 $a(DE-B1597)446487 035 $a(OCoLC)979592495 035 $a(DE-B1597)9781400826940 035 $a(Au-PeEL)EBL445567 035 $a(CaPaEBR)ebr10284147 035 $a(CaONFJC)MIL212946 035 $z(PPN)199244707 035 $a(PPN)187951233 035 $a(FR-PaCSA)88838044 035 $a(MiAaPQ)EBC445567 035 $a(EXLCZ)991000000000756300 100 $a20050330d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aQuadrangular algebras /$fRichard M. Weiss 205 $aCourse Book 210 $aPrinceton, N.J. $cPrinceton University Press$dc2006 215 $a1 online resource (146 p.) 225 1 $aMathematical notes ;$v46 225 1 $aPrinceton paperbacks 300 $aDescription based upon print version of record. 311 $a0-691-12460-4 320 $aIncludes bibliographical references (p. [133]) and index. 327 $t Frontmatter -- $tContents -- $tPreface -- $tChapter One. Basic Definitions -- $tChapter Two. Quadratic Forms -- $tChapter Three. Quadrangular Algebras -- $tChapter Four. Proper Quadrangular Algebras -- $tChapter Five. Special Quadrangular Algebras -- $tChapter Six. Regular Quadrangular Algebras -- $tChapter Seven. Defective Quadrangular Algebras -- $tChapter Eight. Isotopes -- $tChapter Nine. Improper Quadrangular Algebras -- $tChapter Ten. Existence -- $tChapter Eleven. Moufang Quadrangles -- $tChapter Twelve. The Structure Group -- $tBibliography -- $tIndex 330 $aThis book introduces a new class of non-associative algebras related to certain exceptional algebraic groups and their associated buildings. Richard Weiss develops a theory of these "quadrangular algebras" that opens the first purely algebraic approach to the exceptional Moufang quadrangles. These quadrangles include both those that arise as the spherical buildings associated to groups of type E6, E7, and E8 as well as the exotic quadrangles "of type F4" discovered earlier by Weiss. Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras. Formally, the notion of a quadrangular algebra is derived from the notion of a pseudo-quadratic space (introduced by Jacques Tits in the study of classical groups) over a quaternion division ring. This book contains the complete classification of quadrangular algebras starting from first principles. It also shows how this classification can be made to yield the classification of exceptional Moufang quadrangles as a consequence. The book closes with a chapter on isotopes and the structure group of a quadrangular algebra. Quadrangular Algebras is intended for graduate students of mathematics as well as specialists in buildings, exceptional algebraic groups, and related algebraic structures including Jordan algebras and the algebraic theory of quadratic forms. 410 0$aMathematical notes (Princeton University Press) ;$v46. 410 0$aPrinceton paperbacks. 606 $aForms, Quadratic 606 $aAlgebra 610 $aAlgebra over a field. 610 $aAlgebraic group. 610 $aAssociative property. 610 $aAxiom. 610 $aClassical group. 610 $aClifford algebra. 610 $aCommutator. 610 $aDefective matrix. 610 $aDivision algebra. 610 $aFiber bundle. 610 $aGeometry. 610 $aIsotropic quadratic form. 610 $aJacques Tits. 610 $aJordan algebra. 610 $aMoufang. 610 $aNon-associative algebra. 610 $aPolygon. 610 $aPrecalculus. 610 $aProjective plane. 610 $aQuadratic form. 610 $aSimple Lie group. 610 $aSubgroup. 610 $aTheorem. 610 $aVector space. 615 0$aForms, Quadratic. 615 0$aAlgebra. 676 $a512.7/4 686 $a31.20$2bcl 700 $aWeiss$b Richard M$g(Richard Mark),$f1946-$01598284 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910813845503321 996 $aQuadrangular algebras$93920424 997 $aUNINA