Geodesic
Solution of three systems of functional equations related to complex, double and dual numbers
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2023), pp. 42-51

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The article solves three special systems of functional equations arising in the problem of embedding of two-metric phenomenologically symmetric geometries of two sets of rank (3,2) associated with complex, double and dual numbers into a two-metric phenomenologically symmetric geometry of two sets of rank (4,2), which is affine group of transformations on the plane. We are looking for non-degenerate solutions of these systems, which in general are very difficult to find. The problem of determining the set of solutions to these systems, associated with a finite number of Jordan forms of second-order matrices, turned out to be much simpler and more meaningful in the mathematical sense. The solutions obtained have a direct connection with complex, double and dual numbers.
Keywords: geometry of two sets, functional equation, complex, double and dual numbers.
Mots-clés : Jordan form of matrices 
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     author = {V. A. Kyrov and G. G. Mikhailichenko},
     title = {Solution of three systems of functional equations related to complex, double and dual numbers},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {42--51},
     publisher = {mathdoc},
     number = {7},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_7_a4/}
}
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V. A. Kyrov; G. G. Mikhailichenko. Solution of three systems of functional equations related to complex, double and dual numbers. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2023), pp. 42-51. http://geodesic.mathdoc.fr/item/IVM_2023_7_a4/