Infinitesimal CR automorphisms for a class of polynomial models

Martin Kolář; Francine Meylan

Archivum Mathematicum (2017)

  • Volume: 053, Issue: 5, page 255-265
  • ISSN: 0044-8753

Abstract

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In this paper we study infinitesimal CR automorphisms of Levi degenerate hypersurfaces. We illustrate the recent general results of [18], [17], [15], on a class of concrete examples, polynomial models in ℂ 3 of the form ℑ w = ℜ ( P ( z ) Q ( z ) ¯ ) , where P and Q are weighted homogeneous holomorphic polynomials in z = ( z 1 , z 2 ) . We classify such models according to their Lie algebra of infinitesimal CR automorphisms. We also give the first example of a non monomial model which admits a nonlinear rigid automorphism.

How to cite

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Kolář, Martin, and Meylan, Francine. "Infinitesimal CR automorphisms for a class of polynomial models." Archivum Mathematicum 053.5 (2017): 255-265. <http://eudml.org/doc/294258>.

@article{Kolář2017,
abstract = {In this paper we study infinitesimal CR automorphisms of Levi degenerate hypersurfaces. We illustrate the recent general results of [18], [17], [15], on a class of concrete examples, polynomial models in $\mathbb \{C\}^3$ of the form $\Im \; w = \Re (P(z) \overline\{Q(z)\}) $, where $P$ and $Q$ are weighted homogeneous holomorphic polynomials in $z = (z_1, z_2)$. We classify such models according to their Lie algebra of infinitesimal CR automorphisms. We also give the first example of a non monomial model which admits a nonlinear rigid automorphism.},
author = {Kolář, Martin, Meylan, Francine},
journal = {Archivum Mathematicum},
keywords = {Levi degenerate hypersurfaces; finite multitype; polynomial models; infinitesimal CR automorphisms},
language = {eng},
number = {5},
pages = {255-265},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Infinitesimal CR automorphisms for a class of polynomial models},
url = {http://eudml.org/doc/294258},
volume = {053},
year = {2017},
}

TY - JOUR
AU - Kolář, Martin
AU - Meylan, Francine
TI - Infinitesimal CR automorphisms for a class of polynomial models
JO - Archivum Mathematicum
PY - 2017
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 053
IS - 5
SP - 255
EP - 265
AB - In this paper we study infinitesimal CR automorphisms of Levi degenerate hypersurfaces. We illustrate the recent general results of [18], [17], [15], on a class of concrete examples, polynomial models in $\mathbb {C}^3$ of the form $\Im \; w = \Re (P(z) \overline{Q(z)}) $, where $P$ and $Q$ are weighted homogeneous holomorphic polynomials in $z = (z_1, z_2)$. We classify such models according to their Lie algebra of infinitesimal CR automorphisms. We also give the first example of a non monomial model which admits a nonlinear rigid automorphism.
LA - eng
KW - Levi degenerate hypersurfaces; finite multitype; polynomial models; infinitesimal CR automorphisms
UR - http://eudml.org/doc/294258
ER -

References

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