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For each two-dimensional vector space $V$ of commuting $n\times n$ matricesover a field $\mathbb F$ with at least 3 elements, we denote by $\widetilde V$the vector space of all $(n+1)\times(n+1)$ matrices of the form$\left[\begin{smallmatrix}A&*\\0&0\end{smallmatrix}\right]$ with $A\in V$. Weprove the wildness of the problem of classifying Lie algebras $\widetilde V$with the bracket operation $[u,v]:=uv-vu$. We also prove the wildness of theproblem of classifying two-dimensional vector spaces consisting of commutinglinear operators on a vector space over a field.

Wildness of the problems of classifying two-dimensional spaces of commuting linear operators and certain Lie algebras