Wide subcategories of 𝑑-cluster tilting subcategories Page 1 TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 373, Number 4, April 2020, Pages 2281–2309 …

Let D be a triangulated category with a cluster tilting subcategory U. The quotient category
D/U is abelian; suppose that it has finite global dimension. We show that projection from D to …

Tilting theory in cluster categories of hereditary algebras has been developed in [A. Buan, R.
Marsh, M. Reineke, I. Reiten, G. Todorov, Tilting theory and cluster combinatorics, preprint …

We introduce the concept of a pseudo-cluster-tilting subcategory from the viewpoint of the
fact that the quotient of an exact category by a cluster-tilting subcategory is an abelian …

A subcategory W of an abelian category is called wide if it is closed under kernels,
cokernels, and extensions. Wide subcategories are of interest in representation theory …

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 …

Given n≤ d<∞ n≦d<∞, we investigate the existence of algebras of global dimension d
which admit an n-cluster tilting subcategory. We construct many such examples using …

This paper shows a new phenomenon in higher cluster tilting theory. For each positive
integer d, we exhibit a triangulated category 𝖢 with the following properties. On the one …

We study the cluster combinatorics of d-cluster tilting objects in d-cluster categories. Using
mutations of maximal rigid objects in d-cluster categories, which are defined in a similar way …

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