Canonical Isomorphism of Two Lie Algebras Arising in CR-geometry

Research Report MRR98-003

Canonical Isomorphism of Two Lie Algebras Arising in CR-geometry

V. V. Ezhov and A. V. Isaev

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

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