Lie algebras of infinitesimal CR-automorphisms of finite type, holomorphically nondegenerate, weighted homogeneous CR-generic submanifolds of C^N

Abstract

We consider the significant class of holomorphically nondegenerate CR manifolds of finite type that are represented by some weighted homogeneous polynomials and we derive some useful features which enable us to set up a fast effective algorithm to compute their Lie algebras of infinitesimal CR-automorphisms. This algorithm mainly relies upon a natural gradation of the sought Lie algebras, and it also consists in treating separately the related graded components. While some other methods are based on constructing and solving an associated pde systems which become time consuming as soon as the number of variables increases, the new method presented here is based on plain techniques of linear algebra. Furthermore, it benefits from a divide-and-conquer strategy to break down the computations into some simpler sub-computations. Moreover, we consider the new and effective concept of comprehensive Gr\"obner systems which provides us some powerful tools to treat the computations in the parametric cases. The designed algorithm is also implemented in the Maple software.