This article is cited in 4 papers

Phenomenologically symmetrical local Lie groups of transformations of the space $R^s$

V. A. Kyrov

Chair of Physics and Teaching Principles, Gorny Altai State University, Gorno-Altaisk, Russia

Abstract: 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.

UDC: 512.816

Received: 10.01.2007

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:7, 7–16

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