LEADER 02708nam 2200529 450 001 9910817304803321 005 20190812133005.0 010 $a1-4704-5245-6 035 $a(CKB)4100000008483124 035 $a(MiAaPQ)EBC5788260 035 $a(PPN)237290839 035 $a(EXLCZ)994100000008483124 100 $a20190628d2019 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMoufang sets and structurable division algebras /$fLien Boelaert, Tom De Medts, Anastasia Stavrova 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2019] 210 4$dİ2019 215 $a1 online resource (v, 90 pages) $cillustrations 225 1 $aMemoirs of the American Mathematical Society ;$vVolume 259, Number 1245 311 $a1-4704-3554-3 320 $aIncludes bibliographical references. 330 $a"A Moufang set is essentially a doubly transitive permutation group such that each point stabilizer contains a normal subgroup which is regular on the remaining vertices; these regular normal subgroups are called the root groups, and they are assumed to be conjugate and to generate the whole group. It has been known for some time that every Jordan division algebra gives rise to a Moufang set with abelian root groups. We extend this result by showing that every structurable division algebra gives rise to a Moufang set, and conversely, we show that every Moufang set arising from a simple linear algebraic group of relative rank one over an arbitrary field k of characteristic different from 2 and 3 arises from a structurable division algebra. We also obtain explicit formulas for the root groups, the T-map and the Hua maps of these Moufang sets. This is particularly useful for the Moufang sets arising from exceptional linear algebraic groups"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society ;$vVolume 259, Number 1245. 606 $aDivision algebras 606 $aMoufang loops 606 $aJordan algebras 606 $aCombinatorial group theory 615 0$aDivision algebras. 615 0$aMoufang loops. 615 0$aJordan algebras. 615 0$aCombinatorial group theory. 676 $a512.56 686 $a16W10$a20E42$a17A35$a17B60$a17B45$a17Cxx$a20G15$a20G41$2msc 700 $aBoelaert$b Lien$01610188 702 $aStavrova$b Anastasia 702 $aMedts$b Tom de$f1980- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910817304803321 996 $aMoufang sets and structurable division algebras$93937832 997 $aUNINA