Klara Stokes (Umeå University, Sweden) - Triality revisited

 

Sažetak:

An incidence geometry has a duality if there is a correlation permuting two of the types. A duality of order two is also called a polarity. A triality is a correlation of order three, permuting three types. Triality is a classical notion in geometry, associated with an outer automorphism of Lie groups of type D_4. It was first described by E. Study in 1903 and later by E. Cartan in 1925. In 1959, J. Tits classified the trialities with absolute points. These investigations motivated his definition of the generalised polygons; the content of the appendix of the same paper. In this talk I will describe how to use coset geometries to construct examples of incidence geometries with r-alities and prescribed automorphism group. I will also describe how to construct incidence geometries with trialites from maps on surfaces with trialities. This is joint work with Dimitri Leemans.

 

Seminar će se održati kao video konferencija na Zoomu:

https://zoom.us/j/94935481361?pwd=L0dvT0tOWnVodDUydndCd1ErcDl4Zz09

Meeting ID: 949 3548 1361

 

Pozivamo članove Seminara za geometriju i ostale zainteresirane.

 

Vedran Krčadinac