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 ${\Bbb C}^n\times{\Bbb C}^n$ 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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- April 1998
- DOI:
- 10.48550/arXiv.math/9804054
- arXiv:
- arXiv:math/9804054
- Bibcode:
- 1998math......4054E
- Keywords:
-
- Mathematics - Complex Variables;
- 32C16
- E-Print:
- 16 pages, see also http://wwwmaths.anu.edu.au/research.reports/98mrr.html