J. Korean Math. Soc. 2021; 58(1): 173-205
Online first article July 14, 2020 Printed January 1, 2021
https://doi.org/10.4134/JKMS.j200015
Copyright © The Korean Mathematical Society.
Bernhard M\"uhlherr, Richard M. Weiss
Universit\"at Giessen; Tufts University
The spherical buildings associated with absolutely simple algebraic groups of relative rank~$2$ are all Moufang polygons. Tits polygons are a more general class of geometric structures that includes Moufang polygons as a special case. Dagger-sharp Tits $n$-gons exist only for $n=3$, $4$, $6$ and~$8$. Moufang octagons were classified by Tits. We show here that there are no dagger-sharp Tits octagons that are not Moufang. As part of the proof it is shown that the same conclusion holds for a certain class of dagger-sharp Tits quadrangles.
Keywords: Building, Moufang polygon, Tits polygon, exceptional group
MSC numbers: 20E42, 51E12, 51E24
Supported by: This work was partially supported DFG Grant MU 1281/7-1 and by Simons Foundation Collaboration Grant 516364
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd