# Generalised cluster categories from n-Calabi-Yau triples

CAR - Cluster algebras and representation theory

The original definition of cluster algebras by Fomin and Zelevinsky has been categorified and generalised in several ways over the past 20 years. In this talk, we focus on Iyama and Yang’s generalised cluster categories $\mathcal{T}/\mathcal{T}$, coming from $n$-Calabi-Yau triples. In such a construction, $\mathcal{T}$ is a triangulated category with triangulated subcategory $\mathcal{T}{fd}$ and silting subcategory $\mathcal{M}$. Using a different approach from Iyama and Yang, we give a deeper understanding of $\mathcal{T}/\mathcal{T}^{fd}$ and reprove it is a generalised cluster category. In order to do so, we use more classic homological tools such as limits, colimits and a gap theorem.

This talk is part of the Isaac Newton Institute Seminar Series series.