On a category of cluster algebras

Ibrahim Assem (1) , Grégoire Dupont (2) , Ralf Schiffler (3)

1 UdeS - Département de mathématiques [Sherbrooke]
2 UPD7 - Université Paris Diderot - Paris 7
3 UCONN - University of Connecticut

We introduce a category of cluster algebras with fixed initial seeds. This category has countable coproducts, which can be constructed combinatorially, but no products. We characterise isomorphisms and monomorphisms in this category and provide combinatorial methods for constructing special classes of monomorphisms and epimorphisms. In the case of cluster algebras from surfaces, we describe interactions between this category and the geometry of the surfaces.

Mots clés: cluster algebra; cluster morphism

Domaines: Théorie des représentations [math.RT]

Ibrahim Assem, Grégoire Dupont, Ralf Schiffler. On a category of cluster algebras. 2012. ⟨hal-00663953⟩