Moufang sets and structurable division algebras
 Author
 Lien Boelaert, Tom De Medts (UGent) and Anastasia Stavrova
 Organization
 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 taumap 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, 5graded Lie algebra, SIMPLE LIEALGEBRAS, FORMS, PAIRS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU8616798
 MLA
 Boelaert, Lien, et al. “Moufang Sets and Structurable Division Algebras.” MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 259, no. 1245, 2019, doi:10.1090/memo/1245.
 APA
 Boelaert, L., De Medts, T., & Stavrova, A. (2019). Moufang sets and structurable division algebras. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 259(1245). https://doi.org/10.1090/memo/1245
 Chicago authordate
 Boelaert, Lien, Tom De Medts, and Anastasia Stavrova. 2019. “Moufang Sets and Structurable Division Algebras.” MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY 259 (1245). https://doi.org/10.1090/memo/1245.
 Chicago authordate (all authors)
 Boelaert, Lien, Tom De Medts, and Anastasia Stavrova. 2019. “Moufang Sets and Structurable Division Algebras.” MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY 259 (1245). doi:10.1090/memo/1245.
 Vancouver
 1.Boelaert L, De Medts T, Stavrova A. Moufang sets and structurable division algebras. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY. 2019;259(1245).
 IEEE
 [1]L. Boelaert, T. De Medts, 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 taumap and the Hua maps of these Moufang sets. This is particularly useful for the Moufang sets arising from exceptional linear algebraic groups.}}, author = {{Boelaert, Lien and De Medts, Tom and Stavrova, Anastasia}}, isbn = {{9781470435547}}, issn = {{00659266}}, journal = {{MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY}}, keywords = {{Structurable algebra,Jordan algebra,Moufang set,root group,simple algebraic group,5graded Lie algebra,SIMPLE LIEALGEBRAS,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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