Coset geometries with trialities and their reduced incidence graphs. (English) Zbl 07928550
Summary: In this article we explore combinatorial trialities and r-alities of incidence geometries. We give a construction that uses coset geometries to construct examples of incidence geometries with trialities and prescribed automorphism group. We define the reduced incidence graph of the geometry to be the oriented graph obtained as the quotient of the geometry under the triality, and more generally, under an triality. Our chosen examples exhibit interesting features relating the automorphism group of the geometry and the automorphism group of the reduced incidence graphs.
MSC:
| 51A10 | Homomorphism, automorphism and dualities in linear incidence geometry |
| 51E24 | Buildings and the geometry of diagrams |
| 20C33 | Representations of finite groups of Lie type |
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