Cluster tilting vs. weak cluster tilting in Dynkin type A infinity
Abstract
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
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∞.
