English

Incidence geometries with trialities coming from maps with Wilson trialities

Group Theory 2022-09-12 v2 Combinatorics

Abstract

Triality is a classical notion in geometry that arose in the context of the Lie groups of type D4D_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 qq, the group L2(q3){\rm L}_2(q^3) has maps that admit Wilson trialities but no dualities.

Keywords

Cite

@article{arxiv.2208.08215,
  title  = {Incidence geometries with trialities coming from maps with Wilson trialities},
  author = {Dimitri Leemans and Klara Stokes},
  journal= {arXiv preprint arXiv:2208.08215},
  year   = {2022}
}