Two-Dimensional Locally Nash Groups

Author:

Baro Elías1,De Vicente Juan2,Otero Margarita2

Affiliation:

1. Departamento de Álgebra, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain

2. Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Abstract

Abstract We give a classification of connected abelian locally (real) Nash groups of dimension two. We first consider Painlevé’s description of meromorphic maps admitting an algebraic addition theorem and analyse the algebraic dependence of such maps. We then give a classification of connected abelian locally complex Nash groups of dimension two, from which we deduce the corresponding real classification. As a consequence, we obtain a classification of two-dimensional abelian irreducible algebraic groups defined over $\mathbb{R}$.

Funder

Spanish

Grupos UCM

International Program of Excellence in Mathematics at Universidad Autónoma de Madrid

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

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