Article
Ufa Mathematical Journal
Volume 3, Number 2, pp. 85-88
Nonisomorphic Lie algebras admitted by gasdynamic models
Khabirov S.V.
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The group classification of gasdynamic equations by state equation consists from 13 types of finite-dimensional Lie algebras of different dimensions from 11 to 14. Some of types depend on a parameter. There are five pairs of Lie algebras to be equivalent. The equivalent transformations for Lie algebras contain the equivalent transformations for the gasdynamic equations. There are nine nonisomorphic Lie algebras different structures as a result of the tasting on equivalence. One type has 3 different structures for different parameters. Each of these Lie algebras is represented as semidirect sum sixth dimension Abeilian ideal and subalgebra which was decomposed in semidirect or direct sum in turn. The optimal systems for subalgebras are constructed. Addition of Abeilian ideal is done in 6 cases constructing the optimal system. There are 3 Lie algebras of the dimensions 12, 13, 14 for which the optimal systems are not constructed.