Linear Orthosets and Orthogeometries

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Authors

PASEKA Jan VETTERLEIN Thomas

Year of publication 2023
Type Article in Periodical
Magazine / Source International Journal of Theoretical Physics
MU Faculty or unit

Faculty of Science

Citation
Web https://doi.org/10.1007/s10773-023-05282-3
Doi http://dx.doi.org/10.1007/s10773-023-05282-3
Keywords Orthoset; Orthogonality space; Orthogeometry; Hermitian space
Description Anisotropic Hermitian spaces can be characterised as anisotropic orthogeometries, that is, as projective spaces that are additionally endowed with a suitable orthogonality relation. But linear dependence is uniquely determined by the orthogonality relation and hence it makes sense to investigate solely the latter. It turns out that by means of orthosets, which are structures based on a symmetric, irreflexive binary relation, we can achieve a quite compact description of the inner-product spaces under consideration. In particular, Pasch's axiom, or any of its variants, is no longer needed. Having established the correspondence between anisotropic Hermitian spaces on the one hand and so-called linear orthosets on the other hand, we moreover consider the respective symmetries. We present a version of Wigner's Theorem adapted to the present context.
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