Xiaojin Zhang

activity

20092026

τ

-tilting modules over the Auslander algebra of

K [x] / (x^{n})

22 citations · 74 across the 19 of their papers we have counts for

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19 papers · 1 filter

math.RT2026

Relative Suspension and Higher Delooping for Support $τ$ -Tilting Modules

Mingfei Xu, Xiaojin Zhang

We construct relative suspension for the exact category generated by a support $τ$ -tilting module and characterize higher delooping by the units of the resulting adjunction, which…

math.RT2026

The Auslander-Reiten conjecture for algebras with radical cube zero

Xiaojin Zhang, Panyue Zhou

Let $A$ be a split finite-dimensional algebra over a field whose radical $J$ satisfies $J^{3} = 0$ , and let $s$ be the number of isomorphism classes of simple $A$ -modules. We prove tha…

math.RT2026

Self-Orthogonal $τ$ -Tilting Modules and Tilting Modules II: Annihilator Separation

Xiaojin Zhang

Let $A$ be an Artin algebra and let $T$ be a self-orthogonal $τ$ -tilting right $A$ -module. Set $I=\Ann_A(T)$. We prove that \[ \Hom_A(I,T)=0=\Ext_A^n(I,T)\qquad(n\geq 1). \] It fol…

math.RT2026

$τ$ -tilting modules, depth and delooping level

Mingfei Xu, Xiaojin Zhang

Let $A$ be a finite-dimensional basic algebra over an algebraically closed field $K$ , $T$ a finitely generated support $τ$ -tilting right $A$ -module and $B = End_{A} T$ . Denote by…

math.RT2023

A non-vanishing result on the singularity category

Xiao-Wu Chen, Zhi-Wei Li, Xiaojin Zhang +1

We prove that a virtually periodic object in an abelian category gives rise to a non-vanishing result on certain Hom groups in the singularity category. Consequently, for any artin…

math.RT2022

On the number of tilting modules over a class of Auslander algebras

Dan Chen, Xiaojin Zhang

Let $Λ$ be a radical square zero algebra of a Dynkin quiver and let $Γ$ be the Auslander algebra of $Λ$ . Then the number of tilting right $Γ$ -modules is $2^{m - 1}$ if $Λ$ is of $A_{…

math.RT2021

Tau-tilting modules over trivial extenstions

Zhi-Wei Li, Xiaojin Zhang

We study (support) $τ$ -tilting modules over the trivial extensions of finite dimensional algebras. More precisely, we construct two classes of (support) $τ$ -tilting modules in terms…

math.RT2021

A construction of Gorenstein projective tau-tilting modules

Zhi-Wei Li, Xiaojin Zhang

We give a construction of Gorenstein projective $τ$ -tilting modules in terms of tensor products of modules. As a consequence, we give a class of non-self-injective algebras admitti…

math.RT2021

A Bijection theorem for Gorenstein projective τ-tilting modules

Zongzhen Xie, Xiaojin Zhang

We introduce the notions of Gorenstein projective $τ$ -rigid modules, Gorenstein projective support $τ$ -tilting modules and Gorenstein torsion pairs and give a Gorenstein analog to…

math.RT2020★ 1 cited

Classifying tilting modules over the Auslander algebras of radical square zero Nakayama algebras

Xiaojin Zhang

Let $Λ$ be a radical square zero Nakayama algebra with $n$ simple modules and let $Γ$ be the Auslander algebra of $Λ$ . Then every indecomposable direct summand of a tilting $Γ$ -mod…

math.RT2019

Self-orthogonal tau-tilting modules and tilting modules

Xiaojin Zhang

Let $Λ$ be an artin algebra and $T$ a $τ$ -tilting $Λ$ -module. We prove that $T$ is a tilting module if and only if ${\rm Ext}_Λ^{i}(T,\Fac T)=0$ for all $i \geq 1$ , where $\Fac T$ i…

math.RT2019

Three results for tau-rigid modules

Zongzhen Xie, Libo Zan, Xiaojin Zhang

$τ$ -rigid modules are essential in the $τ$ -tilting theory introduced by Adachi, Iyama and Reiten. In this paper, we give equivalent conditions for Iwanaga-Gorenstein algebras with…

math.RT2018★ 16 cited

Tilting modules over Auslander-Gorenstein Algebras

Osamu Iyama, Xiaojin Zhang

For a finite dimensional algebra $Λ$ and a non-negative integer $n$ , we characterize when the set $\tilt_nΛ$ of additive equivalence classes of tilting modules with projective dime…

math.RT2016★ 22 cited

Classifying $τ$ -tilting modules over the Auslander algebra of $K [x] / (x^{n})$

Osamu Iyama, Xiaojin Zhang

We build a bijection between the set $\sttiltΛ$ of isomorphism classes of basic support $τ$ -tilting modules over the Auslander algebra $Λ$ of $K [x] / (x^{n})$ and the symmetric group $…

math.RT2012★ 7 cited

τ-rigid modules for algebras with radical square zero

Xiaojin Zhang

In this paper, we show that for an algebra $Λ$ with radical square zero and an indecomposable $Λ$ -module $M$ such that $Λ$ is Gorenstein of finite type or $τ M$ is $τ$ -rigid, $M$ is…

math.RT2009★ 2 cited

From Auslander Algebras to Tilted Algebras

Zhaoyong Huang, Xiaojin Zhang

This paper has been withdrawn by the authors because it has been combined with "Higher Auslander Algebras Admitting Trivial Maximal Orthogonal Subcategories" (arXiv:0903.0761) toge…

math.RT2009★ 7 cited

Higher Auslander Algebras Admitting Trivial Maximal Orthogonal Subcategories

Zhaoyong Huang, Xiaojin Zhang

For an Artinian $(n - 1)$ -Auslander algebra $Λ$ with global dimension $n (\geq 2)$ , we show that if $Λ$ admits a trivial maximal $(n - 1)$ -orthogonal subcategory of $mod Λ$ , then $Λ$ is…

math.RT2009★ 13 cited

The Existence of Maximal $n$ -Orthogonal Subcategories

Zhaoyong Huang, Xiaojin Zhang

For an $(n - 1)$ -Auslander algebra $Λ$ with global dimension $n$ , we give some necessary conditions for $Λ$ admitting a maximal $(n - 1)$ -orthogonal subcategory in terms of the propert…

math.RT2009★ 6 cited

Trivial Maximal 1-Orthogonal Subcategories For Auslander's 1-Gorenstein Algebras

Zhaoyong Huang, Xiaojin Zhang

Let $Λ$ be an Auslander's 1-Gorenstein Artinian algebra with global dimension two. If $Λ$ admits a trivial maximal 1-orthogonal subcategory of $mod Λ$ , then for any indecomposable…

Relative Suspension and Higher Delooping for Support τ-Tilting Modules

The Auslander-Reiten conjecture for algebras with radical cube zero

Self-Orthogonal τ-Tilting Modules and Tilting Modules II: Annihilator Separation

τ-tilting modules, depth and delooping level

A non-vanishing result on the singularity category

On the number of tilting modules over a class of Auslander algebras

Tau-tilting modules over trivial extenstions

A construction of Gorenstein projective tau-tilting modules

A Bijection theorem for Gorenstein projective τ-tilting modules

Classifying tilting modules over the Auslander algebras of radical square zero Nakayama algebras

Self-orthogonal tau-tilting modules and tilting modules

Three results for tau-rigid modules

Tilting modules over Auslander-Gorenstein Algebras

Classifying τ-tilting modules over the Auslander algebra of K[x]/(xn)

τ-rigid modules for algebras with radical square zero

From Auslander Algebras to Tilted Algebras

Higher Auslander Algebras Admitting Trivial Maximal Orthogonal Subcategories

The Existence of Maximal n-Orthogonal Subcategories

Trivial Maximal 1-Orthogonal Subcategories For Auslander's 1-Gorenstein Algebras

Relative Suspension and Higher Delooping for Support $τ$ -Tilting Modules

Self-Orthogonal $τ$ -Tilting Modules and Tilting Modules II: Annihilator Separation

$τ$ -tilting modules, depth and delooping level

Classifying $τ$ -tilting modules over the Auslander algebra of $K [x] / (x^{n})$

The Existence of Maximal $n$ -Orthogonal Subcategories