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An algorithm to determine the isomorphism classes of 4-dimensional complex Lie algebras. (English) Zbl 0998.17002
An algorithm is given that determines the isomorphism classes of the 4-dimensional complex Lie algebras. The approach is through the \(\text{GL}(V)\)-irreducible decomposition of the polynomial ring of the space \(\Delta^2 V^* \otimes V\) (where \(V=C^4\)) up to degree three. By using the ratio of the eigenvalues of all \(X\), for a sufficiently generic \(X\) in the Lie algebra, three invariants are defined. These three invariants, the dimensions of the derived algebra and second derived algebra and three kinds of covariants determine the isomorphism classes of these algebras.

17B05 Structure theory for Lie algebras and superalgebras
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