# Cluster tilting vs. weak cluster tilting in Dynkin type A infinity

Authors
Type
Published Article
Journal
Forum Mathematicum
Publisher
De Gruyter
Publication Date
Mar 21, 2013
Volume
27
Issue
2
Pages
1117–1137
Identifiers
DOI: 10.1515/forum-2012-0093
Source
De Gruyter
Keywords
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 hand, the d-cluster tilting subcategories of 𝖢 have very simple mutation behaviour: Each indecomposable object has exactly d mutations. On the other hand, the weakly d-cluster tilting subcategories of 𝖢 which lack functorial finiteness can have much more complicated mutation behaviour: For each 0 ≤ ℓ ≤ d - 1, we show a weakly d-cluster tilting subcategory 𝖳 ℓ ${\mathsf {T}_{\ell }}$ which has an indecomposable object with precisely ℓ mutations. The category 𝖢 is the algebraic triangulated category generated by a (d + 1)-spherical object and can be thought of as a higher cluster category of Dynkin type A∞.