查看文章

Let k be a field and let D be a k-linear algebraic triangulated category with split idempotents. Let Σ be the suspension functor of D and let s be a 2-spherical object of D, that is, the morphism space D (s, Σis) is k for i= 0 and i= 2 and vanishes otherwise. Assume that s classically generates D, that is, each object of D can be built from s using (de) suspensions, direct sums, direct summands, and distinguished triangles.

It was proved in [15, thm. 2.1] that D is uniquely determined by these properties. As we will explain, D is a good candidate for a cluster category of Dynkin type A∞. For instance, we show that there is a bijection between the cluster tilting subcategories of D and certain triangulations of the∞-gon.