Two-dimensional simply connected abelian locally Nash groups

TL;DR

This paper classifies two-dimensional simply connected abelian locally Nash groups and characterizes their structures using meromorphic maps with algebraic addition theorems.

Contribution

It provides a complete description of 2D abelian locally Nash groups and characterizes Nash structures on Euclidean spaces via algebraic addition theorems.

Findings

Classification of 2D simply connected abelian locally Nash groups

Characterization of Nash structures on ^n using meromorphic maps

Establishment of a link between Nash groups and algebraic addition theorems

Abstract

The aim of this paper is to give a description of simply connected abelian locally Nash groups of dimension $2$. Along the way we prove that, for any $n\geq 2$, a locally Nash structure over $(\mathbb{R}^n,+)$ can be characterized via a meromorphic map admitting an algebraic addition theorem.