Abstract
All non-similar representations of three-dimensional Lie algebras of operators in ℝ3 are classified. The second-order differential invariants for functions of two variables are calculated for all representations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. H. Ibragimov, Transformations Groups in Mathematical Phisics (Nauka, Moscow, 1983). English transl. Transformation Groups Applied to Mathematical Physics (Riedel, Dordrecht, 1985).
S. V. Khabirov, “Lie-Bäcklund group methods in mathematical physics, “Doctor of Science thesis, Institute of Mathemtics and Mechanics (Sverdlovsk, 1991) (Russian).
G. I. Kruchkovich, “Classification of three-dimentional Riemannian spaces by groups of motions,” UspekhiMat. Nauk 91 (59), 3 (1954).
S. Lie, “Klassification und Integration von gewöhnlichen Differentilgleichungen zwischen x, y, die eine Gruppe von Transformationen gestatten, III,” Archiv forMatematik og Naturvidenskab, Christiania, 8(4), 371 (1883).
P. Medolaghi, “Classificazione delle equationi alle derivate partiali del secondo ordine, che ammetono un gruppo infinito di transformationi puntuali,” Ann. Mat. Pura ed Appl. 1, 229 (1898).
L. V. Ovsyannikov, Group properties of differential equations, Siberian Branch of USSR Academy of Sciences (Novosibirsk, 1962) (Russian).
Author information
Authors and Affiliations
Additional information
Submitted by N.H. Ibragimov
Rights and permissions
About this article
Cite this article
Khabirov, S.V. Classification of three-dimensional Lie algebras in ℝ3 and their second-order differential invariants. Lobachevskii J Math 31, 152–156 (2010). https://doi.org/10.1134/S199508021002006X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S199508021002006X