E-raamat: Moufang Sets and Structurable Division Algebras

"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"--

Boelaert, Medts, and Stavrova show that every structurable division algebra gives rise to a Moufang set, It turns out, they say, that every known proper Moufang set-that is, is not sharply doubly transitive-arises from a structural division algebra, provided that the root groups do not contain elements of order two or three. They cover Moufang sets, structurable algebras, one-invertibility for structurable algebras, simple structurable algebras and simple algebraic groups, Moufang sets and structurable division algebras, and examples. Annotation ©2019 Ringgold, Inc., Portland, OR (protoview.com)