Canonical isomorphism of two Lie algebras arising in CR-geometry

Abstract

We show that the maximal prolongation of a certain algebra associated with a non-degenerate Hermitian form on ${\mathbb{C}}^n\times {\mathbb{C}}^n$ 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.

16 pages, see also http://wwwmaths.anu.edu.au/research.reports/98mrr.html