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- Title
Homological Transfer between Additive Categories and Higher Differential Additive Categories.
- Authors
Tang, Xi; Huang, Zhao Yong
- Abstract
Given an additive category C and an integer n ≥ 2. The higher differential additive category consists of objects X in C equipped with an endomorphism ϵX satisfying ϵ X n = 0 . Let R be a finite-dimensional basic algebra over an algebraically closed field and T the augmenting functor from the category of finitely generated left R-modules to that of finitely generated left R/(tn)-modules. It is proved that a finitely generated left R-module M is τ-rigid (respectively, (support) τ-tilting, almost complete τ-tilting) if and only if so is T(M)as a left R[t]/(tn)-module. Moreover, R is τm-selfinjective if and only if so is R[t]/(tn).
- Subjects
NOETHERIAN rings; ADDITIVES; ENDOMORPHISMS; ALGEBRA; INTEGERS; HOMOLOGICAL algebra
- Publication
Acta Mathematica Sinica, 2024, Vol 40, Issue 5, p1325
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-023-2193-8