On 3-nondegenerate CR manifolds in dimension 7 (I): The transitive case

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Abstract We investigate 3-nondegenerate CR structures in the lowest possible dimension 7, and one of our goals is to prove Beloshapka’s conjecture on the symmetry dimension bound for hypersurfaces in C 4 \mathbb{C}^{4} . We claim that 8 is the maximal symmetry dimension of 3-nondegenerate CR structures in dimension 7, which is achieved on the homogeneous model. This part (I) is devoted to the homogeneous case: we prove that the model is locally the only homogeneous 3-nondegenerate CR structure in dimension 7.