Geodesic
Phenomenologically symmetrical local Lie groups of transformations of the space~$R^s$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2009), pp. 10-21

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In this paper we define a phenomenologically symmetric local Lie group of transformations of an arbitrary-dimensional space. We take as a basis the axiom scheme of the theory of physical structures. Phenomenologically symmetric groups of transformations are nondegenerate both with respect to coordinates and to parameters. We obtain a multipoint invariant of this group of transformations and relate it with Ward quasigroups. We define a substructure of a physical structure as a certain phenomenologically symmetric subgroup of transformations. We establish a criterion for the phenomenological symmetry of the Lie group of transformations and prove the uniqueness of a structure with the minimal rank. We also introduce the notion of a phenomenologically symmetric product of physical structures.
Keywords: physical structure, phenomenologically symmetric Lie group of transformations. 
@article{IVM_2009_7_a1,
     author = {V. A. Kyrov},
     title = {Phenomenologically symmetrical local {Lie} groups of transformations of the space~$R^s$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {10--21},
     publisher = {mathdoc},
     number = {7},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_7_a1/}
}
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V. A. Kyrov. Phenomenologically symmetrical local Lie groups of transformations of the space~$R^s$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2009), pp. 10-21. http://geodesic.mathdoc.fr/item/IVM_2009_7_a1/