Canonical isomorphism of two Lie algebras arising in CR-geometry

1998/04/09 by Vladimir Ezhov, V. V. Ezhov, Ezhov, V. V. +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Holomorphic and Operator Theory #math.CV #msc:32C16

paper · pdf · doi:10.48550/arxiv.math/9804054

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

arxiv created 1998/04/09 · arxiv updated 2009/11/30

Abstract

We show that the maximal prolongation of a certain algebra associated with a non-degenerate Hermitian form on \Bbb Cⁿ×\Bbb Cⁿ 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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• Invariants of elliptic and hyperbolic CR-structures of codimension 2

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