2016
|
Title: Infinite acyclic cluster categories and their combinatorics Abstract: Cluster algebras were introduced by Fomin and Zelevinsky as an algebraic and combinatorial tool for the study of dual canonical bases and total positivity in algebraic groups. A cluster category is a 2-Calabi-Yau triangulated category that categorifies such cluster data. One of the main examples is obtained as an orbit category of the bounded derived category of representations of an acyclic quiver; these categories are known as "acyclic cluster categories." In this talk, I will give examples of acylic cluster categories of infinite rank and show how we can understand these using triangulations of a disc (these are related to Holm-Jorgensen's triangulations of the infinity-gon and Liu-Paquette's triangulations of an infinite strip). This talk is based on joint work with Jan Stovicek. |