On contact and finitely Levi-nondegenerate CR algebras

TL;DR

This paper develops a comprehensive theory linking invariants of CR-manifolds, such as Levi and contact-nondegeneracy, with properties of associated CR-algebras and combinatorial structures in the homogeneous case.

Contribution

It introduces a unified framework connecting CR-manifold invariants with algebraic and combinatorial properties, especially in the parabolic case.

Findings

Established correspondences between CR invariants and algebraic properties.

Developed a classification approach using painted root diagrams.

Extended the theory to arbitrary CR codimension and homogeneous settings.

Abstract

We study CR-manifolds of arbitrary CR codimension, mainly focusing on Levi and contact-nondegeneracy and depth. We investigate these and other invariants in the locally homogeneous case, developing a comprehensive theory which establishes correspondences with related properties of the associated CR-algebras and, in the parabolic case, with the combinatorics of their cross-marked painted root diagrams.