02708nam 2200529 450 991081730480332120190812133005.01-4704-5245-6(CKB)4100000008483124(MiAaPQ)EBC5788260(PPN)237290839(EXLCZ)99410000000848312420190628d2019 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierMoufang sets and structurable division algebras /Lien Boelaert, Tom De Medts, Anastasia StavrovaProvidence, Rhode Island :American Mathematical Society,[2019]©20191 online resource (v, 90 pages) illustrationsMemoirs of the American Mathematical Society ;Volume 259, Number 12451-4704-3554-3 Includes bibliographical references."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"--Provided by publisher.Memoirs of the American Mathematical Society ;Volume 259, Number 1245.Division algebrasMoufang loopsJordan algebrasCombinatorial group theoryDivision algebras.Moufang loops.Jordan algebras.Combinatorial group theory.512.5616W1020E4217A3517B6017B4517Cxx20G1520G41mscBoelaert Lien1610188Stavrova AnastasiaMedts Tom de1980-MiAaPQMiAaPQMiAaPQBOOK9910817304803321Moufang sets and structurable division algebras3937832UNINA