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

New examples of 2‐nondegenerate real hypersurfaces in CN$\mathbb {C}^N$ with arbitrary nilpotent symbols

“…Notice also that if 𝑆 𝑗,𝑘 = 0 for all 𝑗 + 𝑘 = 𝑛 − 1, then Φ does not define a uniformly 2-nondegenerate hypersurface, that is, noting (26),…”

“…In particular, [27, part 3 of Theorem 6.2] implies that ℂ ⊗ 𝔥𝔬𝔩(𝑀 0 , 0) has the ℤ-grading conferred by ad 𝑉 0 with negative parts given by (38). Vanishing of the positive weight components follows immediately from [26,Theorem 3.7] and [27, Theorem 6.2]. We require 𝑛 > 4 for this last conclusion so that [26, Theorem 3.7] applies.…”

“…We require 𝑛 > 4 for this last conclusion so that [26, Theorem 3.7] applies. Specifically, [26,Theorem 3.7] does not apply if 𝑛 = 3 or 𝑛 = 4 because it is in exactly these cases that their structure's CR symbol is regular. □ Corollary 6.3.…”