Optimal system for the sum of two ideals admitted by the hydrodynamic type equations

Abstract

We introduce the rules for constructing the optimal system of the dissimilar subalgebras for the sum of two ideals for which the optimal systems are known. As a result, we give the dissimilar subalgebra for five not yet considered Lie algebra admitted by the hydrodynamic type equations. It completes the listing of the subalgebras for the Lie algebras in the group classification of the gas dynamic models by the state equation.