Jian Liu

collaborators

9 papers

math.CT2026

A pre-triangulated category which is not triangulated

Xiao-Wu Chen, Jian Liu, Xue-Song Lu +1

In this article, we construct an explicit pre-triangulated category which is not a triangulated category. Its underlying additive category is the category of finitely generated pro…

math.GT2026

Khovanov homology: pro-tangles, derived colimits and spectral sequences

Jian Liu, Kefeng Liu, Li Shen

This paper introduces pro-tangles, a natural generalization of classical tangles, which are functors from the Boolean cube to Bar-Natan's cobordism category. By employing the simpl…

math.RA2026

Cotorsion pairs, thick subcategories, and finitely generated Gorenstein projective modules

Souvik Dey, Jian Liu, Xue-Song Lu

Let $R$ be a noetherian algebra over a Cohen--Macaulay ring $S$ admitting a canonical module $I ¨ $ , and assume that $R$ is maximal Cohen--Macaulay over $S$ . We prove that the catego…

math.RT2026

Base change of (Gorenstein) transpose, k-torsionfree modules, and quasi-faithfully flat extensions

Jian Liu

Let $I ¨ : R \to A$ be a finite ring homomorphism, where $R$ is a two-sided Noetherian ring, and let $M$ be a finitely generated left $A$ -module. Under suitable homologi…

math.AC2025

On local rings of finite syzygy representation type

Souvik Dey, Kaito Kimura, Jian Liu +1

Let $R$ be a commutative Noetherian local ring. We characterize when its completion has an isolated singularity, thereby strengthening the Dao-Takahashi refinement of the Auslander…

math.CO2025

Multi-scale symmetry analysis in molecular structures

Jing-Wen Gao, Yunan He, Jian Liu

Topological data analysis (TDA), as a relatively recent approach, has demonstrated great potential in capturing the intrinsic and robust structural features of complex data. While…