Calabi-Yau triangulated categories Page 483 Calabi-Yau triangulated categories Bernhard
Keller 1 Introduction These notes reflect the contents of three lectures given at the workshop …

The concept of cluster tilting gives a higher analogue of classical Auslander correspondence
between representation-finite algebras and Auslander algebras. The n-Auslander–Reiten …

We study the oriented exchange graph EG∘(Γ NQ) of reachable hearts in the finite-
dimensional derived category D (Γ NQ) of the CY-N Ginzburg algebra Γ NQ associated to an …

We prove the existence of an m-cluster tilting object in a generalized m-cluster category
which is (m+ 1)-Calabi–Yau and Hom-finite, arising from an (m+ 2)-Calabi–Yau dg algebra …

Cluster algebras were introduced by Fomin-Zelevinsky in 2002 in order to give a
combinatorial framework for phenomena occurring in the context of algebraic groups …

In this paper we establish a connection between ribbon graphs and Brauer graphs. As a
result, we show that a compact oriented surface with marked points gives rise to a unique …

We define mutation on coloured quivers associated to tilting objects in higher cluster
categories. We show that this operation is compatible with the mutation operation on the …

For a finite-dimensional hereditary algebra H, we consider: exceptional sequences in mod
H, silting objects in the bounded derived category D, and m-cluster tilting objects in the m …

Let W be a finite crystallographic reflection group. The generalized Catalan number of W
coincides both with the number of clusters in the cluster algebra associated to W, and with …

We study maximal m-rigid objects in the m-cluster category CHm associated with a finite
dimensional hereditary algebra H with n nonisomorphic simple modules. We show that all …