Local structure of 2-dimensional solvable Lie algebra actions on the plane (Q372747)

This paper studies in detail the local action of 2-dimensional non-abelian solvable algebras on the plane. The author divides it into 3 cases according to the dimension of the \(g\)-orbit of the point on the plane is \(0, 1, 2\), called the singular case, weak singular case, and transitive case, respectively. Above all, the author gives equivalent classes of 2-dimensional solvable algebras actions on the plane.