Symmetry algebras of polynomial models in complex dimension three

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.

Keywords

infinitesimal CR automorphisms, Levi degenerate manifolds, Catlin multitype

2010 Mathematics Subject Classification

32V35, 32V40

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

Received 20 April 2021

Accepted 30 August 2021

Published 13 May 2022