Year: 2026
Type: preprint
Abstract: We construct relative suspension for the exact category generated by a support $τ$-tilting module and characterize higher delooping by the units of the resulting adjunction, which are the generalizations of Gélinas's results in Adv. Math.(2022). We prove that comparison with ordinary higher delooping requires a shift of one in the index. More precisely, for every $k,d\ge1$, there is a module whose ordinary $k$-delooping level is zero and whose relative level is $d$. We also prove that tensor induction preserves the relative constructions and higher delooping levels on induced modules. As an application, we study cyclic Nakayama algebras with arbitrary local coefficients and automorphism twists. Their left and right little and big finitistic dimensions and ordinary and derived delooping levels all equal the finitistic dimension of the underlying Nakayama algebra.
Source: arXiv (Cornell University)
Authors: Xu, Mingfei, Zhang, Xiaojin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2985936811, G5646081729
OpenAlex ID: W7214985213