Deciding isomorphism of Lie algebras

When doing calculations with Lie algebras one of the main problems is to decide whether two given Lie algebras are isomorphic. A partial solution to this problem is obtained by calculating structural invariants. There is also a direct method available which involves the computation of Grobner bases. In this paper we combine these approaches. The resulting method is applied to the problem of identifiying a small dimensional Lie algebra as a member of existing list of Lie algebras