Baro González, ElíasOtero Domínguez, Margarita2024-10-162024-10-162021https://doi.org/10.1093/qmath/haab021https://hdl.handle.net/20.500.14352/109032We give a classification of connected abelian locally (real) Nash groups of dimension two. We first consider Painlev´e’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 R.engjournal articlehttps://academic.oup.com/qjmath/article-abstract/73/1/93/6247787?redirectedFrom=fulltextrestricted accessÁlgebra1201 Álgebra