2 citations · 6 across the 16 of their papers we have counts for
17 papers
Geometric Realizations of Capability Spaces of Large Models and Zigzag Persistent Homology
Yu-Zhe Liu, Shengda Liu, Jianyong Pi +1
We propose a topological model for capability changes during large-model training. The model represents knowledge states and preregistered capability probes as subcomplexes of a fi…
Module-valued ordinary differential equations and structure of solution spaces
Shengda Liu, Yu-Zhe Liu, Keyu Tao
We define and study ordinary differential equations (ODEs) for functions valued in a Banach module over a finite-dimensional -algebra by using the tensor of B…
Igusa-Todorov properties of recollements of abelian categories
Peiru Yang, Yajun Ma, Yu-Zhe Liu
In this paper, we investigate the behavior of Igusa-Todorov properties under recollements of abelian categories. In particular, we study how the Igusa-Todorov distances of the cate…
Normed representations of weight quivers
Yu-Zhe Liu
Let and be two tensor rings given by weight quivers. We introduce norms for tensor rings and -bimodules, and define an important category in this p…
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 BD-algebra and CM-Auslander algebra for a gentle algebra and their representation types
Mengdie Zhang, Yu-Zhe Liu, Chao Zhang
Let be a gentle algebra, and and be its BD-gentle algebra and CM-Auslander algebra, respectively. In this paper, we show that the representation-finiteness of , …
Homological dimensions over almost gentle algebras
Demin Wang, Zhaoyong Huang, Yu-Zhe Liu
We provide a method for computing the global dimension and self-injective dimension of almost gentle algebras,and prove that an almost gentle algebra is Gorenstein if it satisfies…
Normed modules, integral sequences, and integrals with variable upper limits
Miantao Liu, Yu-Zhe Liu, Shengda Liu
This paper provides a new categorification of the Lebesgue integral with variable upper limits by using normed modules over finite-dimensional -algebras and the c…
Three homological invariants under cleft extensions
Yajun Ma, Junling Zheng, Yu-Zhe Liu
In this paper, we investigate the behavior of Igusa-Todorov distances, extension and Rouquier dimensions under cleft extensions of abelian categories. We apply our results to Morit…
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…
Normed modules and The Stieltjes integrations of functions defined on finite-dimensional algebras
Hanpeng Gao, Shengda Liu, Yu-Zhe Liu +1
We define integrals for functions on finite-dimensional algebras, adapting methods from Leinster's research. This paper discusses the relationships between the integrals of functio…
Normed modules and the categorification of integrations, series expansions, and differentiations
Yu-Zhe Liu, Shengda Liu, Zhaoyong Huang +1
We explore the assignment of norms to -modules over a finite-dimensional algebra , resulting in the establishment of normed -modules. Our primary cont…
The Cohen-Macaulay Auslander algebras of string algebras
Yu-Zhe Liu, Chao Zhang
The Cohen-Macaulay Auslander algebra of any string algebra is explicitly constructed in this paper. Furthermore, we show that a class of special string algebras, which are called t…
A negative answer to Complement Question for presilting complexes
Yu-Zhe Liu, Yu Zhou
In this paper using a geometric model we show that there is a presilting complex over a finite dimensional algebra, which is not a direct summand of a silting complex.
There are no strictly shod algebras in hereditary gentle algebras
Houjun Zhang, Yu-Zhe Liu
We prove that there are no strictly shod algebras in hereditary gentle algebras by geometric models. As an application, we give a classification of the silted algebras for Dynkin t…
Classification silted algebras for a quiver of Dynkin type via geometric models
Yu-Zhe Liu, Houjun Zhang
Let $\Q$ be the quiver of Dynkin type with linear orientation and $A_{n}=k\Q$. In this paper, we give a complete classification of the silted algebras of type $A_{n}…
Homological Dimensions of Gentle Algebras via Geometric Models
Yu-Zhe Liu, Hanpeng Gao, Zhaoyong Huang
Let be a finite dimensional basic algebra over an algebraically closed field which is a gentle algebra with the marked ribbon surface $(\mathcal{S}_A,\mathcal{M}_A,Γ_A…