JournalsprimsVol. 35, No. 2pp. 249–261

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
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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.

Cite this article

Vladimir V. Ezhov, Alexander V. Isaev, Canonical Isomorphism of Two Lie Algebras Arising in <em>CR</em>-geometry. Publ. Res. Inst. Math. Sci. 35 (1999), no. 2, pp. 249–261

DOI 10.2977/PRIMS/1195143951