Maximal Dimension of Groups of Symmetries of Homogeneous 2-nondegenerate CR Structures of Hypersurface Type with a 1-dimensional Levi Kernel

Abstract

We prove that for every n ≥ 3 the sharp upper bound for the dimension of the symmetry groups of homogeneous, 2-nondegenerate, (2n + 1)-dimensional CR manifolds of hypersurface type with a 1-dimensional Levi kernel is equal to n2 + 7, and simultaneously establish the same result for a more general class of structures characterized by weakening the homogeneity condition. This supports Beloshapka’s conjecture stating that hypersurface models with a maximal finite dimensional group of symmetries for a given dimension of the underlying manifold are Levi nondegenerate.