On functional bases of the first-order differential invariants for non-conjugate subgroups of the Poincaré group P(1,4)
Abstract
It is established which functional bases of the first-order differential invariants of the splitting and non-splitting subgroups of the Poincaré group P(1,4) are invariant under the subgroups of the extended Galilei group G̃(1,3) ⊂ P(1,4). The obtained sets of functional bases are classified according to dimensions.
References
V.M. Fedorchuk, V.I. Fedorchuk, On the differential first-order invariants for the non-splitting subgroups of the generalized Poincaré group P(1, 4), Ann. Acad. Pedagog. Crac. Stud. Math. 4 (2004), 65-74.
##plugins.generic.googleScholarLinks.settings.viewInGS##
V.M. Fedorchuk, V.I. Fedorchuk, On differential invariants of first- and second-order of the splitting subgroups of the generalized Poincaré group P(1, 4), Symmetry in nonlinear mathematical physics, Part 1, 2 (Kyiv, 2001), Pr. Inst. Mat. Nats. Akad. Nauk Ukr. Mat. Zastos. 43, Part 1, vol. 2, Natsionalna Akademiia Nauk Ukrainy, Instytut Matematyky, Kiev, 2002, 140-144.
##plugins.generic.googleScholarLinks.settings.viewInGS##
V.M. Fedorchuk, Nonsplit subalgebras of the Lie algebra of the generalized Poincaré group P(1, 4), Ukrain. Mat. Zh. 33 (1981), no. 5, 696-700.
##plugins.generic.googleScholarLinks.settings.viewInGS##
V.M. Fedorčuk, Split subalgebras of the Lie algebra of the generalized Poincaré group P(1, 4), Ukrain. Mat. Zh. 31 (1979), no. 6, 717-722.
##plugins.generic.googleScholarLinks.settings.viewInGS##
V.I. Fushchich, L.F. Barannik, A.F. Barannik, Podgruppovoi analiz grupp Galileya, Puankare i reduktsiya nelineinykh uravnenii, “Naukova Dumka”, Kiev, 1991.
##plugins.generic.googleScholarLinks.settings.viewInGS##
W.I. Fushchich, A. F. Barannik, L. F. Barannik, V. M. Fedorchuk, Continuous subgroups of the Poincaré group P(1, 4), J. Phys. A: Math. Gen 18 (1985), no. 15, 2893-2899.
##plugins.generic.googleScholarLinks.settings.viewInGS##
W.I. Fushchich, A.G. Nikitin, Symmetries of equations of quantum mechanics, Allerton Press Inc., New York, 1994.
##plugins.generic.googleScholarLinks.settings.viewInGS##
W.I. Fushchych, Representations of the complete inhomogeneous de Sitter group and equations in the five-dimensional approach. I, Theor. Math. Phys. 4 (1970), no. 3, 890-907.
##plugins.generic.googleScholarLinks.settings.viewInGS##
V.G. Kadyshevskii, A new approach to the theory of electromagnetic interactions, Fiz. Èlementar. Chastits i Atom. Yadra 11 (1980), no. 1, 5–39.
##plugins.generic.googleScholarLinks.settings.viewInGS##
S. Lie, Ueber Differentialinvarianten, Math. Ann. 24 (1884), no. 4, 537-578.
##plugins.generic.googleScholarLinks.settings.viewInGS##
S. Lie, G. Scheffers, Vorlesungen über continuierliche Gruppen mit geometrischen und anderen Anwendungen, Teubner, Leipzig, 1893.
##plugins.generic.googleScholarLinks.settings.viewInGS##
P.J. Olver, Applications of Lie groups to differential equations, Graduate Texts in Mathematics, vol. 107, Springer-Verlag, New York, 1986.
##plugins.generic.googleScholarLinks.settings.viewInGS##
L.V. Ovsiannikov, Group analysis of differential equations, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1982.
##plugins.generic.googleScholarLinks.settings.viewInGS##
