Canonical isomorphism of two Lie algebras arising in CR-geometry

V. V. Ezhov; A. V. Isaev

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Canonical isomorphism of two Lie algebras arising in CR-geometry

V. V. Ezhov·A. V. Isaev

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Abstract

We show that the maximal prolongation of a certain algebra associated with a non-degenerate Hermitian form on ${\Bbb C}^n\times{\Bbb C}^n$ with values in ${\Bbb R}^k$ is canonically isomorphic to the Lie algebra of infinitesimal holomorphic automorphisms of the corresponding quadric in ${\Bbb C}^{n+k}$. This fact creates a link between different approaches to the equivalence problem for Levi-nondegenerate strongly uniform CR-manifolds.

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V. V. Ezhov, A. V. Isaev. 1998-04-09. Canonical isomorphism of two Lie algebras arising in CR-geometry. https://arxiv.org/abs/math/9804054

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