On G-stable n-rigid objects in (n + 2)-angulated categories

Abstract

Let [Formula: see text] be a Krull–Schmidt Hom-finite [Formula: see text]-angulated category with [Formula: see text]-suspension functor [Formula: see text] and Serre functor [Formula: see text]. Assume [Formula: see text] is an Oppermann–Thomas cluster tilting object in [Formula: see text] and [Formula: see text] is an auto-equivalence of [Formula: see text]. Let [Formula: see text]. We investigate some classes of [Formula: see text]-stable [Formula: see text]-rigid objects in [Formula: see text], prove that the stability of [Formula: see text]-rigid objects can be transferred to some pairs for [Formula: see text], and we obtain a new higher version of the Adachi–Iyama–Reiten bijection. As applications, we generalize the Jacobsen–J[Formula: see text]rgensen bijection to the general case (not necessarily [Formula: see text]-Calabi–Yau), and we recover a work due to Yang, Zhang and Zhu.