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An isomorphism of the Lie algebras L 11 admissible by the full Boltzmann kinetic equation with an arbitrary differential cross section and by the Euler gas dynamics system of equations with a general state equation is set up. The similarity is also proved between extended algebras L 12 admissible by the same equations for specified power-like intermolecular potentials and for polytropic gas. This allows the solution of the problem of classification of the full Boltzmann equation invariant H-solutions using an optimal system of subalgebras known for the Euler system. Representations of essentially different H-solutions of the spatially inhomogeneous Boltzmann equation with one and two independent invariant variables in the explicit form are obtained on this basis.

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