# On transitive contact and $CR$ algebras

## TL;DR

This paper proves that under certain contact structure conditions, the automorphisms of locally homogeneous CR manifolds form a finite dimensional Lie group.

## Contribution

It establishes a new condition based solely on contact structure that guarantees finite dimensionality of CR automorphism groups.

## Key findings

- CR automorphism groups are finite dimensional under the new contact condition
- The condition depends only on the underlying contact structure
- Results apply to locally homogeneous CR manifolds

## Abstract

We consider locally homogeneous $CR$ manifolds and show that, under a condition only depending on their underlying contact structure, their $CR$ automorphisms form a finite dimensional Lie group.