Linear Orthosets and Orthogeometries

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Publikace nespadá pod Filozofickou fakultu, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
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PASEKA Jan VETTERLEIN Thomas

Rok publikování 2023
Druh Článek v odborném periodiku
Časopis / Zdroj International Journal of Theoretical Physics
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://doi.org/10.1007/s10773-023-05282-3
Doi http://dx.doi.org/10.1007/s10773-023-05282-3
Klíčová slova Orthoset; Orthogonality space; Orthogeometry; Hermitian space
Popis 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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