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Moufang sets and structurable division algebras

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Abstract
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 tau-map and the Hua maps of these Moufang sets. This is particularly useful for the Moufang sets arising from exceptional linear algebraic groups.
Keywords
Structurable algebra, Jordan algebra, Moufang set, root group, simple algebraic group, 5-graded Lie algebra, SIMPLE LIE-ALGEBRAS, FORMS, PAIRS

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MLA
De Medts, Tom, Lien Boelaert, and Anastasia Stavrova. “Moufang Sets and Structurable Division Algebras.” MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY 259.1245 (2019): n. pag. Print.
APA
De Medts, T., Boelaert, L., & Stavrova, A. (2019). Moufang sets and structurable division algebras. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 259(1245).
Chicago author-date
De Medts, Tom, Lien Boelaert, and Anastasia Stavrova. 2019. “Moufang Sets and Structurable Division Algebras.” Memoirs of the American Mathematical Society 259 (1245).
Chicago author-date (all authors)
De Medts, Tom, Lien Boelaert, and Anastasia Stavrova. 2019. “Moufang Sets and Structurable Division Algebras.” Memoirs of the American Mathematical Society 259 (1245).
Vancouver
1.
De Medts T, Boelaert L, Stavrova A. Moufang sets and structurable division algebras. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY. 2019;259(1245).
IEEE
[1]
T. De Medts, L. Boelaert, and A. Stavrova, “Moufang sets and structurable division algebras,” MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 259, no. 1245, 2019.
@article{8616798,
  abstract     = {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 tau-map and the Hua maps of these Moufang sets. This is particularly useful for the Moufang sets arising from exceptional linear algebraic groups.},
  author       = {De Medts, Tom and Boelaert, Lien and Stavrova, Anastasia},
  isbn         = {9781470435547},
  issn         = {0065-9266},
  journal      = {MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY},
  keywords     = {Structurable algebra,Jordan algebra,Moufang set,root group,simple algebraic group,5-graded Lie algebra,SIMPLE LIE-ALGEBRAS,FORMS,PAIRS},
  language     = {eng},
  number       = {1245},
  pages        = {91},
  title        = {Moufang sets and structurable division algebras},
  url          = {http://dx.doi.org/10.1090/memo/1245},
  volume       = {259},
  year         = {2019},
}

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