Download this article
 Download this article For screen
For printing
Recent Issues
Volume 18
Volume 16
Volume 15
Volume 14
Volume 13
Volume 12
Volume 11
Volume 10
Volume 9
Volume 8
Volume 6+7
Volume 5
Volume 4
Volume 3
Volume 2
Volume 1
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN (electronic): 2640-7345
ISSN (print): 2640-7337
Author Index
To Appear
Other MSP Journals
Incidence geometries with trialities coming from maps with Wilson trialities

Dimitri Leemans and Klara Stokes

Vol. 20 (2023), No. 2-3, 325–340

Triality is a classical notion in geometry that arose in the context of the Lie groups of type D4. 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 L2(q3) has maps that admit Wilson trialities but no dualities.

In memoriam Jacques Tits, whose mathematicshave been a great source of inspiration in our work

triality, maps, incidence geometry, projective special linear groups
Mathematical Subject Classification
Primary: 20C33, 51A10, 51E24
Received: 31 August 2022
Revised: 17 January 2023
Accepted: 15 February 2023
Published: 13 September 2023
Dimitri Leemans
Département de Mathématique
Université libre de Bruxelles
Algèbre et Combinatoire
Klara Stokes
Department of Mathematics and Mathematical Statistics
Umeå Universitet