TY - BOOK

T1 - Moufang Sets and Structurable Division Algebras

AU - Boelaert, Lien

AU - De Medts, Tom

AU - Stavrova, Anastasia

N1 - Publisher Copyright: © 2019 American Mathematical Society.

PY - 2019/5

Y1 - 2019/5

N2 - 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.

AB - 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.

KW - 5-graded Lie algebra

KW - Jordan algebra

KW - Moufang set

KW - Root group

KW - Simple algebraic group

KW - Structurable algebra

KW - FORMS

KW - root group

KW - simple algebraic group

KW - SIMPLE LIE-ALGEBRAS

KW - PAIRS

UR - http://www.scopus.com/inward/record.url?scp=85065617459&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/moufang-sets-structurable-division-algebras

U2 - 10.1090/memo/1245

DO - 10.1090/memo/1245

M3 - Book

SN - 978-1-4704-3554-7

VL - 259

T3 - Memoirs of the American Mathematical Society

BT - Moufang Sets and Structurable Division Algebras

PB - American Mathematical Society

ER -