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.
In memoriam Jacques Tits, whose
mathematicshave been a great source of inspiration in our
work
Keywords
triality, maps, incidence geometry, projective special
linear groups
