Characterization of Real-Analytic Infinitesimal CR Automorphisms for a Class of Hypersurfaces in \(\Bbb C^4\)

In this chapter, motivated by the work of Kim and Kolar in [7] for the case of pseudoconvex models that are sums of squares of polynomials, we study the Lie algebra \(\mathfrak {g}\) of real-analytic infinitesimal CR automorphisms of a model hypersurface \(M_0\) given by 1 \(\displaystyle {} M_0= \{(z,w) \in \mathbb C^{3} \times \mathbb C \ | \ \mathsf {Im}\, w= P\bar Q + Q\bar P + R\bar R \}, \) where \(P,\) Q, and R are homogeneous polynomials. In particular, we classify \(M_0\) with respect to the description of its nilpotent rotations when \(P,\) Q, and R are monomials. We also give an example of a model \(M_0\) for which the real dimension of its generalized (exotic) rotations is \(3.\)