CLUSTER ALGEBRAS ARISING FROM INFINITY-GON

Abstract

We introduce a handy construction of cluster algebras of type A∞, we give a complete classification of the cluster algebras arising from the infinitygon, and finally we construct the category of the diagonals of the infinity-gon and show that it is triangle-equivalent to the infinite cluster category of type A∞ described by Holm and Jørgensen.

Keywords

• Cluster algebras, infinity-gon, infinite cluster category