Geometry of free cyclic submodules over ternions

Details Geometry of free cyclic submodules over ternions Geometry of free cyclic submodules over ternions

2010-12-07

arxiv.org/abs/1012.1459v1

Mathematics

Rings and Algebras

This work was carried out within the framework of the Scientific and Technological Cooperation Poland-Austria 2010--2011

Scientific paper

Given the algebra $T$ of ternions (upper triangular $2\times 2$ matrices) over a commutative field $F$ we consider as set of points of a projective line over $T$ the set of all free cyclic submodules of $T^2$. This set of points can be represented as a set of planes in the projective space over $F^6$. We exhibit this model, its adjacency relation, and its automorphic collineations. Despite the fact that $T$ admits an $F$-linear antiautomorphism, the plane model of our projective line does not admit any duality.

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