Exceptional groups of relative rank one and Galois involutions of Tits quadrangles

Bernhard Mühlherr and Richard M. Weiss

Vol. 307 (2020), No. 2, 391–454

DOI: 10.2140/pjm.2020.307.391

Abstract

Weshow that every Moufang set associated with one of the Tits indices ${}^2{E}_{6,1}^{29}$, $E_{7,1}^{48}$, $E_{8,1}^{91}$ or $F_{4,1}^{21}$ in arbitrary characteristic can be obtained as the fixed point building of a Galois involution acting on a Tits quadrangle parametrized by a quadrangular algebra. This result is used to calculate an explicit formula for the structure map of an arbitrary Moufang set in this class.

Keywords

building, Moufang set, Tits polygon, exceptional group

Mathematical Subject Classification 2010

Primary: 20E42, 51E12, 51E24

Milestones

Received: 27 September 2019

Revised: 9 April 2020

Accepted: 26 April 2020

Published: 4 September 2020