DOI

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.

Язык оригиналаанглийский
ИздательAmerican Mathematical Society
Число страниц102
Том259
Издание1245
ISBN (электронное издание)978-1-4704-5245-2
ISBN (печатное издание)978-1-4704-3554-7
DOI
СостояниеОпубликовано - мая 2019

Серия публикаций

НазваниеMemoirs of the American Mathematical Society
ИздательAmerican Mathematical Society
1245
Том259
ISSN (печатное издание)0065-9266

    Предметные области Scopus

  • Прикладная математика
  • Математика (все)

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