TILTING MODULES OF FINITE PROJECTIVE DIMENSION: SEQUENTIALLY STATIC AND COSTATIC MODULES

2002 ◽  
Vol 01 (03) ◽  
pp. 295-305 ◽  
Author(s):  
ALBERTO TONOLO
Keyword(s):  
Projective Dimension ◽  
Tilting Module ◽  
Tilting Modules ◽  
Finite Projective Dimension

In [5], Miyashita introduced tilting modules of finite projective dimension. A tilting module AV of projective dimension less or equal than r furnishes r + 1 equivalences between subcategories of A-Mod and End V-Mod: we call static and costatic the modules in A-Mod and End V-Mod, respectively, involved in these equivalences. In this paper we characterize the modules in A-Mod and End V-Mod which have a filtration with static and costatic factors, respectively.

REPETITIVE EQUIVALENCES AND TILTING THEORY

2019 ◽  
pp. 1-40
Author(s):  
JIAQUN WEI
Keyword(s):  
Projective Dimension ◽  
Derived Categories ◽  
Tilting Module ◽  
Tilting Modules ◽  
Tilting Theory ◽  
Finite Projective Dimension ◽  
Morita Theory ◽  
Wakamatsu Tilting Module ◽  
Stable Module

Let $R$ be a ring and $T$ be a good Wakamatsu-tilting module with $S=\text{End}(T_{R})^{op}$ . We prove that $T$ induces an equivalence between stable repetitive categories of $R$ and $S$ (i.e., stable module categories of repetitive algebras $\hat{R}$ and ${\hat{S}}$ ). This shows that good Wakamatsu-tilting modules seem to behave in Morita theory of stable repetitive categories as that tilting modules of finite projective dimension behave in Morita theory of derived categories.

scholarly journals PROPERLY STRATIFIED ALGEBRAS AND TILTING

2005 ◽  
Vol 92 (1) ◽  
pp. 29-61 ◽  
Author(s):  
ANDERS FRISK ◽  
VOLODYMYR MAZORCHUK
Keyword(s):  
Projective Dimension ◽  
Finitistic Dimension ◽  
Tilting Module ◽  
Tilting Modules ◽  
Category Of Modules ◽  
Cotilting Modules ◽  
Contravariantly Finite ◽  
Properly Stratified Algebras ◽  
Stratified Algebra ◽  
Generalized Tilting Module

We study the properties of tilting modules in the context of properly stratified algebras. In particular, we answer the question of when the Ringel dual of a properly stratified algebra is properly stratified itself, and show that the class of properly stratified algebras for which the characteristic tilting and cotilting modules coincide is closed under taking the Ringel dual. Studying stratified algebras whose Ringel dual is properly stratified, we discover a new Ringel-type duality for such algebras, which we call the two-step duality. This duality arises from the existence of a new (generalized) tilting module for stratified algebras with properly stratified Ringel dual. We show that this new tilting module has a lot of interesting properties; for instance, its projective dimension equals the projectively defined finitistic dimension of the original algebra, it guarantees that the category of modules of finite projective dimension is contravariantly finite, and, finally, it allows one to compute the finitistic dimension of the original algebra in terms of the projective dimension of the characteristic tilting module.

scholarly journals Tilting modules of finite projective dimension and a generalization of ∗-modules

2003 ◽  
Vol 268 (2) ◽  
pp. 404-418 ◽  
Author(s):  
Jiaqun Wei ◽  
Zhaoyong Huang ◽  
Wenting Tong ◽  
Jihong Huang
Keyword(s):  
Projective Dimension ◽  
Tilting Modules ◽  
Finite Projective Dimension

scholarly journals Tilting modules and dominant dimension with respect to injective modules

2020 ◽  
Author(s):  
Takahide Adachi ◽  
Mayu Tsukamoto
Keyword(s):  
Projective Dimension ◽  
Sufficient Condition ◽  
Tilting Modules ◽  
Dominant Dimension ◽  
Gorenstein Algebras ◽  
Injective Modules ◽  
Finite Projective Dimension

Abstract In this paper, we study a relationship between tilting modules with finite projective dimension and dominant dimension with respect to injective modules as a generalization of results of Crawley-Boevey–Sauter, Nguyen–Reiten–Todorov–Zhu and Pressland–Sauter. Moreover, we give characterizations of almost n-Auslander–Gorenstein algebras and almost n-Auslander algebras by the existence of tilting modules. As an application, we describe a sufficient condition for almost 1-Auslander algebras to be strongly quasi-hereditary by comparing such tilting modules and characteristic tilting modules.

Modules of finite projective dimension and cocovers

1996 ◽  
Vol 306 (1) ◽  
pp. 445-457 ◽  
Author(s):  
Dieter Happel ◽  
Luise Unger
Keyword(s):  
Projective Dimension ◽  
Finite Projective Dimension

CLOSE NEIGHBORS IN THE QUIVER OF TILTING MODULES

2008 ◽  
Vol 07 (03) ◽  
pp. 379-392
Author(s):  
DIETER HAPPEL
Keyword(s):  
Representation Type ◽  
Tilting Module ◽  
Tilting Modules ◽  
Hereditary Algebra ◽  
Simple Modules ◽  
Finite Dimensional ◽  
Wild Representation Type ◽  
Local Properties

For a finite dimensional hereditary algebra Λ local properties of the quiver [Formula: see text] of tilting modules are investigated. The existence of special neighbors of a given tilting module is shown. If Λ has more than 3 simple modules it is shown as an application that Λ is of wild representation type if and only if [Formula: see text] is a subquiver of [Formula: see text].

Wakamatsu tilting modules over ring extension

2019 ◽  
Vol 18 (10) ◽  
pp. 1950198
Author(s):  
Zhen Zhang ◽  
Jiaqun Wei
Keyword(s):  
Ring Extension ◽  
Tilting Module ◽  
Tilting Modules ◽  
Wakamatsu Tilting Module ◽  
Extension Ring

For a ring [Formula: see text], an extension ring [Formula: see text], and a fixed right [Formula: see text]-module [Formula: see text], we prove the induced left [Formula: see text]-module [Formula: see text] is a Wakamatsu tilting module when [Formula: see text] is a Wakamatsu tilting module.

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