Equivalence of Vector Field Realizations of Lie Algebras from the Lie Group Point of View
The equivalence of vector field realizations of Lie algebras is considered from the viewpoint of the Lie algebra and also from the corresponding (local) Lie group. It is shown that for some stages in the establishment of the equivalence things are simpler in the case of the Lie group. A lemma about the equivalence of the sum of realizations is proposed.
MN is grateful for the hospitality extended to her at the Department of mathematics, FNSPE, Czech Technical University in Prague, where part of this work was done. SP is grateful for the hospitality extended to him at the Institute of Mathematics of NAS of Ukraine.
- 1.L.P. Eisenhart, Continuous groups of transformations, (Dover Publications, New York, 1961), pp. 79–80.Google Scholar
- 2.D. Gromada, S. Pošta, On classification of Lie algebra realizations, math-ph/1703.00808v1, (2017), 20 pages.Google Scholar
- 3.S. Lie, Theory of Transformation groupes I, ed., transl. J. Merker, (Springer, 2015), pp. 341–378.Google Scholar
- 4.M. Nesterenko, S. Pošta, Comparison of realizations of Lie algebras, Procedings of the XXVth International Conference on Integrable Systems and Quantum symmetries, J. Phys.: Conf. Ser. (2018), to appear.Google Scholar