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135   $aur|n|---|||||
181   $ctxt
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183   $acr
200 10$aQuadrangular algebras$b[electronic resource] /$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
608   $aElectronic books.
615  0$aForms, Quadratic.
615  0$aAlgebra.
676   $a512.7/4
686   $a31.20$2bcl
700   $aWeiss$b Richard M$g(Richard Mark),$f1946-$01043570
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910454722303321
996   $aQuadrangular algebras$92492902
997   $aUNINA