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arXiv · 2208.08215

Incidence geometries with trialities coming from maps with Wilson trialities

Dimitri Leemans·Klara Stokes
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Abstract

Triality is a classical notion in geometry that arose in the context of the Lie groups of type $D_4$. Another notion of triality, Wilson triality, appears in the context of reflexible maps. We build a bridge between these two notions, showing how to construct an incidence geometry with a triality from a map that admits a Wilson triality. We also extend a result by Jones and Poulton, showing that for every prime power $q$, the group ${\rm L}_2(q^3)$ has maps that admit Wilson trialities but no dualities.

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Dimitri Leemans, Klara Stokes. 2022-08-17. Incidence geometries with trialities coming from maps with Wilson trialities. https://arxiv.org/abs/2208.08215

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