Associative algebras in $CR$-geometry

TL;DR

This paper presents a method to algebraize CR-manifolds and their automorphisms, explores applications through examples, and discusses potential extensions to other areas of geometry and analysis.

Contribution

It introduces a new algebraization procedure for CR-manifolds and automorphisms, with applications and discussions on broader implications.

Findings

Algebraization procedure successfully applied to examples.

Questions and challenges in algebraizing CR-manifolds are identified.

Potential for extending algebraization to other geometric and analytical contexts.

Abstract

A procedure for the algebraization of a $CR$-manifold and its holomorphic automorphisms is described. Examples of the application of algebraization are considered. Questions arising in connection with the algebraization of a $CR$-manifold are formulated. The possibilities of extending this procedure to other branches of geometry and analysis are discussed.