Vol. 307, No. 2, 2020

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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
Abstract

Weshow that every Moufang set associated with one of the Tits indices ${}^{2}\phantom{\rule{-0.17em}{0ex}}{E}_{6,1}^{29}$, ${E}_{7,1}^{48}$, ${E}_{8,1}^{91}$ 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.

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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
Authors
 Bernhard Mühlherr Mathematisches Institut Universität Giessen Germany Richard M. Weiss Mathematics Tufts University Medford, MA United States