We show that the maximal prolongation of a certain algebra associated with a non-degenerate Hermitian form on \mathbb{C}
n×\mathbb{C}
n with values in \mathbb{R}
k is canonically isomorphic to the Lie algebra of infinitesimal holomorphic automorphisms of the corresponding quadric in \mathbb{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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