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 C of the bounded derived category of a Dynkin quiver, which is highly reminiscent of the cluster category. The category C is (-1)-Calabi-Yau. Holm and Jorgensen introduced a family of triangulated categories generated by $w$-spherical objects. When $w\ge 2$, these may be regarded as higher cluster categories of type A infinity. When $w\le -1$, they are higher analogues of the orbit category C. In this paper, 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 new geometric model for the higher versions of the orbit category C.

17 pages, 4 figures

References in corpus (1)

• On triangulated orbit categories