LEADER 03894nam 22007093 450 001 9910959854403321 005 20231110232530.0 010 $a9781470470180 010 $a1470470187 035 $a(MiAaPQ)EBC6852909 035 $a(Au-PeEL)EBL6852909 035 $a(CKB)20667665800041 035 $a(RPAM)22496890 035 $a(OCoLC)1292081387 035 $a(EXLCZ)9920667665800041 100 $a20220117d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTits Polygons 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2022. 210 4$dİ2022. 215 $a1 online resource (132 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.275 300 $a"January 2022, volume 275, number 1352 (sixth of 6 numbers)." 311 08$aPrint version: Mühlherr, Bernhard Tits Polygons Providence : American Mathematical Society,c2022 9781470451011 320 $aIncludes bibliographical references and index. 327 $aTits polygons -- Tits hexagons -- Groups of relative rank 1 -- Appendix / by Holger P. Petersson. 330 $a"We introduce the notion of a Tits polygon, a generalization of the notion of a Moufang polygon, and show that Tits polygons arise in a natural way from certain configurations of parabolic subgroups in an arbitrary spherical buildings satisfying the Moufang condition. We establish numerous basic properties of Tits polygons and characterize a large class of Tits hexagons in terms of Jordan algebras. We apply this classification to give a "rank 2" presentation for the group of F-rational points of an arbitrary exceptional simple group of F-rank at least 4 and to determine defining relations for the group of F-rational points of an an arbitrary group of Frank 1 and absolute type D4, E6, E7 or E8 associated to the unique vertex of the Dynkin diagram that is not orthogonal to the highest root. All of these results are over a field of arbitrary characteristic"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aMoufang loops 606 $aJordan algebras 606 $aBuildings (Group theory) 606 $aGraph theory 606 $aPolygons 606 $aNonassociative rings and algebras -- Jordan algebras (algebras, triples and pairs) -- Exceptional Jordan structures$2msc 606 $aGroup theory and generalizations -- Structure and classification of infinite or finite groups -- Groups with a $BN$-pair; buildings$2msc 606 $aGeometry -- Finite geometry and special incidence structures -- Generalized quadrangles, generalized polygons$2msc 606 $aGeometry -- Finite geometry and special incidence structures -- Buildings and the geometry of diagrams$2msc 615 0$aMoufang loops. 615 0$aJordan algebras. 615 0$aBuildings (Group theory) 615 0$aGraph theory. 615 0$aPolygons. 615 7$aNonassociative rings and algebras -- Jordan algebras (algebras, triples and pairs) -- Exceptional Jordan structures. 615 7$aGroup theory and generalizations -- Structure and classification of infinite or finite groups -- Groups with a $BN$-pair; buildings. 615 7$aGeometry -- Finite geometry and special incidence structures -- Generalized quadrangles, generalized polygons. 615 7$aGeometry -- Finite geometry and special incidence structures -- Buildings and the geometry of diagrams. 676 $a512/.2 686 $a17C40$a20E42$a51E12$a51E24$2msc 700 $aMühlherr$b Bernhard$01802346 701 $aWeiss$b Richard M$0504133 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910959854403321 996 $aTits Polygons$94348008 997 $aUNINA