JournalsprimsVol. 35 , No. 2DOI 10.2977/prims/1195143951

Canonical Isomorphism of Two Lie Algebras Arising in <em>CR</em>-geometry

  • Vladimir V. Ezhov

    The University of Adelaide, Australia
  • Alexander V. Isaev

    Australian National University, Canberra, Australia
Canonical Isomorphism of Two Lie Algebras Arising in <em>CR</em>-geometry cover

Abstract

We show that the maximal prolongation of a certain algebra associated with a non-degenerate Hermitian form on ℂ_n_ x ℂ_n_ with values in ℝ_k_ is canonically isomorphic to the Lie algebra of infinitesimal holomorphic automorphisms of the corresponding quadric in ℂ_n_+k. This fact creates a link between different approaches to the equivalence problem for Levi-nondegenerate strongly uniform CR-manifolds.