Lie algebras of infinitesimal automorphisms for the model manifolds of general classes ${\sf II}$, ${\sf III_2}$ and ${\sf IV_2}$

TL;DR

This paper computes the Lie algebras of infinitesimal automorphisms for specific classes of CR-model manifolds using Cartan's equivalence method, advancing understanding of their symmetry structures.

Contribution

It provides explicit determination of automorphism Lie algebras for models in classes ${ m II}$, ${ m III_2}$, and ${ m IV_2}$, which was previously unknown.

Findings

Explicit Lie algebra structures for each class

Application of Cartan's equivalence method to CR-models

Enhanced classification of CR-manifold symmetries

Abstract

We determine the Lie algebras of infinitesimal automorphisms for the models of the CR-manifolds belonging to general classes ${\sf II}$, ${\sf III_2}$ and ${\sf IV_2}$ through Cartan's equivalence method.