Resumen de Maximal abelian group actions on the ordered real line and their digital representations
Investigations on commuting functions, done by many authors into diverse directions, lead to the search for maximal abelian groups of maps respecting a certain structure. Here we investigate the example of automorphisms of the linear ordering $ (\mathbb{R}, \leq) $. Nontrivial phenomena occur which might be typical for much more general situations. In our example one can use results from the theory of lattice ordered groups (in particular the Conrad-Harvey-Holland Theorem) to get representations by real valued functions. This leads to a set of invariants which, modulo a notion of equivalence which is rather well understood, classifies all maximal abelian subgroups of the automorphism group of $ (\mathbb{R}, \leq) $ up to conjugation.
