A functional realization of sl(3, R) providing minimal Vessiot-Guldberg-Lie algebras of nonlinear second-order ordinary differential equations as proper subalgebras

作者：Campoamor Stur**erg R^*

来源：Journal of Mathematical Physics, 2016, 57(6): 063508.

DOI：10.1063/1.4954255

A functional realization of the Lie algebra sl (3, R) as a Vessiot-Guldberg-Lie algebra of second order differential equation (SODE) Lie systems is proposed. It is shown that a minimal Vessiot-Guldberg-Lie algebra LVG is obtained from proper subalgebras of sl (3, R) for each of the SODE Lie systems of this type by particularization of one functional and two scalar parameters of the sl (3, R)-realization. The relation between the various Vessiot-Guldberg-Lie algebras by means of a limiting process in the scalar parameters further allows to define a notion of contraction of SODE Lie systems. Published by AIP Publishing.

• 出版日期2016-6