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arXiv · 1012.1459

Geometry of free cyclic submodules over ternions

Hans Havlicek·Andrzej Matras·Mark Pankov
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Abstract

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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Hans Havlicek, Andrzej Matras, Mark Pankov. 2010-12-07. Geometry of free cyclic submodules over ternions. https://doi.org/10.1007/s12188-011-0060-5

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