14 papers
Relative Derived Delooping Levels and -Tilting Modules
Hanpeng Gao, Dajun Liu, Houjun Zhang
Let be an essentially small idempotent-complete exact category with enough projective objects. We develop derived delooping levels in . We apply this fra…
Higher Cotorsion Pairs on Image-Nilpotent \(η\)-Extensions
Dajun Liu, Hanpeng Gao
Let \(\cB\) be an abelian category with enough projective and injective objects, and let $ \cA=\cB\ltimes_η\sF $ be an \(η\)-extension induced by a right exact endofunctor \(\sF\).…
Projectively Wakamatsu Tilting Modules over One-Point Extensions
Dajun Liu, Jiaxuan Feng, Hanpeng Gao
Let be the one-point extension of an algebra by a -module . We establish a method to lift projectively Wakamatsu tilting (PWT) modules from to…
A characterization of IE-closed subcategories via -tilting theory
Hanpeng Gao, Dajun Liu, Yu-Zhe Liu
Enomoto and Sakai classified functorially finite IE-closed subcategories over hereditary algebras in terms of twin rigid modules. Their approach uses the hereditary assumption esse…
Some functors preserving exceptionality
Dajun Liu, Hanpeng Gao, Yu-Zhe Liu
We constructed some tensor functors that send each exceptional sequence in a module category to another exceptional sequence in another module category by using split extensions an…
On the Gorensteiness of string algebras
Houjun Zhang, Dajun Liu, Yu-Zhe Liu
In this paper, we give a description of the self-injective dimension of string algebras and obtain a necessary and sufficient condition for a string algebra to be Gorenstein.
Recollements and Gorenstein projective modules for gentle algebras
Yu-Zhe Liu, Dajun Liu, Xin Ma
Let be a gentle algebra. We provide a bijection between non-projective indecomposable Gorenstein projective modules over and special recolleme…
Quotients of extriangulated categories induced by selforthogonal subcategories
Peiyu Zhang, Yiwen Shi, Dajun Liu +2
Let C be an extriangulated category. We prove that two quotient categories of extriangu?lated categories induced by selforthogonal subcategories are equivalent to module categories…
Silting objects and torsion pairs in comma categories
Peiyu Zhang, Xinyu Wang, Dajun Liu +2
In this paper, we first give a characterization of silting objects in the comma category Assume that C1 and C2 are two subcategories of left R-modules, D1 and D2 be two subcategori…
Star modules with respect to balanced pair
Peiyu Zhang, Dajun Liu, Jiaqun Wei
n this article, firstly, we introduce the notion of star modules with respect to a balanced pair and obtain some properties. We mainly give the relationship between n-X star module…
Balanced pairs and tilting modules in recollement
Peiyu Zhang, Dajun Liu, Jiaqun Wei
In this paper, firstly, we mainly study the relationship of balanced pairs among three Abelian categories in a recollement. As an application of admissible balanced pairs, we intro…
Gorenstein projective objects and recollements of Abelian categories
Peiyu Zhang, Qianqian Shu, Dajun Liu
In this paper, we study the relationship of Gorenstein projective objects among three Abelian categories in a recollement. As an application, we introduce the relation of -Goren…
Relative AR-correspondence, co-t-structure and silting pair
Peiyu Zhang, Dajun Liu, Jiaqun Wei
As a generalization of tilting pair, which was introduced by Miyashita in \cite{YM}, the notion of silting pair is introduced in this paper. The authors extends a characterization…
Gorenstein syzygy objects in extriangulated categories
Peiyu Zhang, Ming Chen, Dajun Liu +1
We give the definition of Gorenstein syzygy objects in extriangulated categories and obtain a characterization. For a recollement of extriangulated categories, we mainly show that…