Abstract
Abstract Optimal classifications of Lie algebras of some well-known equations under their group of inner automorphism are re-considered. By writing vector fields of some known Lie algebras in the abstract format, we have proved that there exist explicit isomorphism between Lie algebras and sub-algebras which have already been classified. The isomorphism between Lie algebras is useful in the sense that the classifications of sub-algebras of dimension ≤4 have previously been carried out in literature. These already available classifications can be used to write classification of any Lie algebra of dimension ≤4. As an example, the explicit isomorphism between Lie algebra of variant Boussinesq system and sub-algebra A 3,5 1 / 2 ${A}_{3,5}^{1/2}$ is proved, and subsequently, optimal sub-algebras up to dimension four are obtained. Besides this, some other examples of Lie algebras are also considered for explicit isomorphism.
Published Version
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