We show that the maximal prolongation of a certain algebra associated with a non-degenerate Hermitian form on ℂ_n_ x ℂ_n_ with values in ℝ_k_ is canonically isomorphic to the Lie algebra of infinitesimal holomorphic automorphisms of the corresponding quadric in ℂ_n_+k. This fact creates a link between different approaches to the equivalence problem for Levi-nondegenerate strongly uniform CR-manifolds.
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Vladimir V. Ezhov, Alexander V. Isaev, Canonical Isomorphism of Two Lie Algebras Arising in <em>CR</em>-geometry. Publ. Res. Inst. Math. Sci. 35 (1999), no. 2, pp. 249–261DOI 10.2977/PRIMS/1195143951