13 citations · 37 across the 7 of their papers we have counts for
7 papers
The algebraic stability for persistent Laplacians
Jian Liu, Jingyan Li, Jie Wu
The stability of topological persistence is one of the fundamental issues in topological data analysis. Numerous methods have been proposed to address the stability of persistent m…
On the Cayley-persistence algebra
Wanying Bi, Jingyan Li, Jian Liu +1
In this paper, we introduce a persistent (co)homology theory for Cayley digraph grading. We give the algebraic structures of Cayley-persistence object. Specifically, we consider th…
Triangulated categories of periodic complexes and orbit categories
Jian Liu
We investigate the triangulated hull of the orbit categories of the perfect derived category and the bounded derived category of a ring concerning the power of the suspension funct…
Exceptional complete intersection maps of local rings
Srikanth B. Iyengar, Janina C. Letz, Jian Liu +1
This work concerns surjective maps of commutative noetherian local rings with kernel generated by a regular sequence that is part of a minimal generating set for t…
A partial converse ghost lemma for the derived category of a commutative noetherian ring
Jian Liu, Josh Pollitz
In this article a condition is given to detect the containment among thick subcategories of the bounded derived category of a commutative noetherian ring. More precisely, for a com…
Singular equivalences induced by bimodules and quadratic monomial algebras
Xiao-Wu Chen, Jian Liu, Ren Wang
We investigate the problem when the tensor functor by a bimodule yields a singular equivalence. It turns out that this problem is equivalent to the one when the Hom functor given b…
Duality and symmetry of complexity over complete intersections via exterior homology
Jian Liu, Josh Pollitz
We study homological properties of a locally complete intersection ring by importing facts from homological algebra over exterior algebras. One application is showing that the thic…