Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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DAGGER-SHARP TITS OCTAGONS

  • Muhlherr, Bernhard (Mathematisches Institut Universitat Giessen) ;
  • Weiss, Richard M. (Department of Mathematics Tufts University)
  • Received : 2020.01.10
  • Accepted : 2020.04.08
  • Published : 2021.01.01
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Abstract

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.

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Acknowledgement

This work was partially supported DFG Grant MU 1281/7-1 and by Simons Foundation Collaboration Grant 516364.

References

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