Hom-configurations in triangulated categories generated by spherical objects

Abstract

Hom- and Riedtmann configurations were studied in the context of stable module categories of selfinjective algebras and a certain orbit category C1(Q) of the bounded derived category of a Dynkin quiver Q, which is highly reminiscent of the cluster category. The category C1(Q) is (−1)-Calabi–Yau. In this paper we consider triangulated categories generated by w-spherical objects, for w<0, and higher versions of the orbit category C1(An), denoted by C|w|(An). These categories have also negative Calabi–Yau dimension. We classify the (higher) Hom- and Riedtmann configurations for these categories, and link them with noncrossing partitions in the case w=−1. Along the way, we obtain a geometric model for C|w|(An).