SL(3,R) as the group of symmetry transformations for all one-dimensional linear systems. II. Realizations of the Lie algebra
Copyright policy )SL(3,R) as the group of symmetry transformations for all one-dimensional linear systems. II. Realizations of the Lie algebra
The two-dimensional space-time realizations of the Lie algebra of SL(3,R) are obtained, when the group acts as the maximal point symmetry group of any given one-dimensional Newtonian linear system. It is shown that these realizations are isomorphic with the realization of the Lie algebra of the projective group in the plane. Next an active point of view is introduced, and SL(3,R) is interpreted as a group of mappings that transform one admissible world line of the system into another. Thus a new mechanical realization of the sl(3,R) algebra comes to the fore. Some miscellaneous examples are included.
two-dimensional space-time realizations of the Lie algebra of SL(3,R), SL(3,R), Linear ordinary differential equations and systems, two-dimensional space-time realizations of the Lie algebra of, Newtonian linear system, maximal point symmetry group
two-dimensional space-time realizations of the Lie algebra of SL(3,R), SL(3,R), Linear ordinary differential equations and systems, two-dimensional space-time realizations of the Lie algebra of, Newtonian linear system, maximal point symmetry group
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