Nonisomorphic Lie algebras admitted by gasdynamic models

Group classification of gasdynamic equations by the state equation consists of 13 types of finite-dimensional Lie algebras of different dimensions, from 11 to 14. Some types depend on a parameter. Five pairs of Lie algebras appear to be equivalent. The equivalent transformations for Lie algebras contain the equivalent transformations for gasdynamic equations. The equivalence test resulted in nine nonisomorphic Lie algebras with different structures. One type has 3 different structures for different parameters. Each of these Lie algebras is represented as a semidirect sum of a six-dimensional Abeilian ideal with a subalgebra, which is decomposed into a semidirect or direct sum in its turn. The optimal systems for subalgebras are constructed. The Abeilian ideal is added in 6 cases while constructing the optimal system. There remain 3 Lie algebras of the dimensions 12, 13, 14 for which the optimal systems are not constructed.