Abstract
We introduce the higher version of Adachi-Iyama-Reiten's support τ-tilting pairs, which are regarded as a generalization of maximal τn-rigid pairs in the sense of Jacobsen-Jørgensen. Assume that C is an (n+2)-angulated category with an n-suspension functor Σn and T is an Opperman-Thomas cluster tilting object. We prove that relative n-rigid objects in C are in bijection with τn-rigid pairs in the n-abelian category C/addΣnT, and relative maximal n-rigid objects in C are in bijection with support τn-tilting pairs. We also prove that relative n-self-perpendicular objects are in bijection with maximal τn-rigid pairs. These results generalize work for C being 2n-Calabi-Yau by Jacobsen-Jørgensen and work for n=1 by Yang-Zhu.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
