Pure and Applied Mathematics Quarterly

Volume 18 (2022)

Number 2

Special issue in honor of Joseph J. Kohn on the occasion of his 90th birthday

Guest Editors: J.E. Fornaess, Stanislaw Janeczko, Duong H. Phong, and Stephen S.T. Yau

Symmetry algebras of polynomial models in complex dimension three

Pages: 639 – 656

DOI: https://dx.doi.org/10.4310/PAMQ.2022.v18.n2.a13


Martin Kolář (Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic)


We consider the Lie algebra of infinitesimal CR automorphisms of a real hypersurface at a point of Levi degeneracy. As a main result, we give a complete classification of symmetry algebras of dimension at least six for polynomial models of finite Catlin multitype in $\mathbb{C}^3$. As a consequence, this also provides understanding of “exotic” higher order symmetries, which violate $2$‑jet determination.


infinitesimal CR automorphisms, Levi degenerate manifolds, Catlin multitype

2010 Mathematics Subject Classification

32V35, 32V40

The author is supported by the GACR grant GA21-09220S.

Received 20 April 2021

Accepted 30 August 2021

Published 13 May 2022