Incidence geometries with trialities coming from maps with Wilson trialities

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 $L_{2} (q^{3})$ has maps that admit Wilson trialities but no dualities.

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

PDF Access Denied

We have not been able to recognize your IP address 18.219.103.183 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

triality, maps, incidence geometry, projective special linear groups

Mathematical Subject Classification

Primary: 20C33, 51A10, 51E24

Milestones

Received: 31 August 2022

Revised: 17 January 2023

Accepted: 15 February 2023

Published: 13 September 2023

Authors

Dimitri Leemans
Département de Mathématique Université libre de Bruxelles Algèbre et Combinatoire Brussels Belgium

Klara Stokes
Department of Mathematics and Mathematical Statistics Umeå Universitet Umeå Sweden

Vol. 20, No. 2-3, 2023

Dimitri Leemans and Klara Stokes

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors