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\begin{document}$\mathfrak{L}_m $\end{document} be the scheme of the laws defined by the Jacobi identities on \documentclass[12pt]{minimal}
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\begin{document}$\mathbb{K}^m $\end{document} with \documentclass[12pt]{minimal}
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\begin{document}$\mathbb{K}$\end{document} a field. A deformation of \documentclass[12pt]{minimal}
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\begin{document}$\mathfrak{g} \in \mathfrak{L}_m $\end{document}, parametrized by a local ring A, is a local morphism from the local ring of \documentclass[12pt]{minimal}
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\begin{document}$\mathfrak{L}_m $\end{document} at ϕm to A. The problem of classifying all the deformation equivalence classes of a Lie algebra with given base is solved by “versal” deformations. First, we give an algorithm for computing versal deformations. Second, we prove there is a bijection between the deformation equivalence classes of an algebraic Lie algebra ϕm = R ⋉ φn in \documentclass[12pt]{minimal}
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\begin{document}$\mathfrak{L}_m $\end{document} and its nilpotent radical φn in the R-invariant scheme \documentclass[12pt]{minimal}
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\begin{document}$\mathfrak{L}_{n}^{\rm R} $\end{document} with reductive part R, under some conditions. So the versal deformations of ϕm in \documentclass[12pt]{minimal}
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\begin{document}$\mathfrak{L}_m $\end{document} are deduced from those of φn in \documentclass[12pt]{minimal}
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\begin{document}$\mathfrak{L}_{n}^{\rm R} $\end{document}, which is a more simple problem. Third, we study versality in central extensions of Lie algebras. Finally, we calculate versal deformations of some Lie algebras.
