Abstract:
We consider a six-dimensional Lie algebra with two nonzero commutation relations. We proved that there are 21 types of such non-similar Lie algebras in the space of first-order differential operators on a space of four variables. Then we construct canonical forms of basis operators for the realizations in the space of four variables of these types of non-similar Lie algebras. The number of second-order differential invariants and additional invariant relations was calculated for each basis operators. The general forms of the corresponding invariant systems of three second-order ordinary differential equations are obtained for fifteen non-similar Lie algebras. An illustrative example is given to show how the results can be used for integration of a system of three second-order ordinary differential equations admitting considered six-dimensional Lie algebra.
Keywords:Lie algebra, differential invariants, invariant system of ordinary differential equations.
