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arXiv · 1307.3484

Adjacency preservers on invertible hermitian matrices II

Marko Orel
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Abstract

Maps that preserve adjacency on the set of all invertible hermitian matrices over a finite field are characterized. It is shown that such maps form a group that is generated by the maps $A\mapsto PAP^{\ast}$, $A\mapsto A^{\sigma}$, and $A\mapsto A^{-1}$, where $P$ is an invertible matrix, $P^{\ast}$ is its conjugate transpose, and $\sigma$ is an automorphism of the underlying field. Bijectivity of maps is not an assumption but a conclusion. Moreover, adjacency is assumed to be preserved in one directions only. The main result and author's previous result [16] are applied to characterize maps that preserve the `speed of light' on (a) finite Minkowski space-time and (b) the complement of the light cone in finite Minkowski space-time.

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Marko Orel. 2013-07-10. Adjacency preservers on invertible hermitian matrices II. https://doi.org/10.1016/j.laa.2014.10.033

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