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 . 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 , the group 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}
}