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. The authors extend this result by showing that every structurable division algebra gives rise to a Moufang set, and conversely, they 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. The authors 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.
About the Author
Lien Boelaert, Ghent University, Belgium.Tom De Medts, Ghent University, Belgium.Anastasia Stavrova, St. Petersburg State University, Saint Petersburg, Russia.
- Contributor: Lien Boelaert
- Imprint: American Mathematical Society
- ISBN13: 9781470435547
- Number of Pages: 88
- Packaged Dimensions: 178x254mm
- Format: Paperback
- Publisher: American Mathematical Society
- Release Date: 2019-08-30
- Series: Memoirs of the American Mathematical Society
- Binding: Paperback / softback
- Biography: Lien Boelaert, Ghent University, Belgium.Tom De Medts, Ghent University, Belgium.Anastasia Stavrova, St. Petersburg State University, Saint Petersburg, Russia.
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