Infinitesimal symmetries of weakly pseudoconvex manifolds

We consider weakly pseudoconvex hypersurfaces with polynomial models in $${\mathbb {C}}^N$$ and their symmetry algebras. In the most prominent case of special models, given by sums squares polynomials, we give complete classification. particular, prove that such manifolds do not admit any nonlinear symmetries, depending only on complex tangential variables, nor they real or nilpotent linear symmetries. This leads to a sharp 2-jet determination result for local automorphisms. also partial results general more detailed description graded components dimension three. The provide an important necessary step solving equivalence problem manifolds.