Cluster algebras arising from the infinity-gon

Abstract

We introduce a handy construction of cluster algebras of type ${\mathbb{A}}_{\infty }$, we give a complete classification of the cluster algebras arising from the infinity-gon, 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 ${\mathbb{A}}_{\infty }$ described by Holm and Jørgensen.

23 pages

References in corpus (2)

• On triangulated orbit categories
• Cluster structures for 2-Calabi-Yau categories and unipotent groups