Selfinjective algebras and tilting theory

Representation Theory I Finite Dimensional Algebras - Lecture Notes in Mathematics ◽

10.1007/bfb0075270 ◽

1986 ◽

pp. 272-307 ◽

Cited By ~ 2

Author(s):

Hiroyuki Tachikawa

Keyword(s):

Tilting Theory

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Handbook of Tilting Theory

10.1017/cbo9780511735134 ◽

2007 ◽

Cited By ~ 25

Keyword(s):

Tilting Theory

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The tilting theory of contraction algebras

Advances in Mathematics ◽

10.1016/j.aim.2020.107372 ◽

2020 ◽

Vol 374 ◽

pp. 107372

Author(s):

Jenny August

Keyword(s):

Tilting Theory

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KOSZUL DUALITY FOR STRATIFIED ALGEBRAS II. STANDARDLY STRATIFIED ALGEBRAS

Journal of the Australian Mathematical Society ◽

10.1017/s1446788710001497 ◽

2010 ◽

Vol 89 (1) ◽

pp. 23-49 ◽

Cited By ~ 9

Author(s):

VOLODYMYR MAZORCHUK

Keyword(s):

Complete Picture ◽

Projective Modules ◽

Koszul Duality ◽

Tilting Theory

AbstractWe give a complete picture of the interaction between the Koszul and Ringel dualities for graded standardly stratified algebras (in the sense of Cline, Parshall and Scott) admitting linear tilting (co)resolutions of standard and proper costandard modules. We single out a certain class of graded standardly stratified algebras, imposing the condition that standard filtrations of projective modules are finite, and develop a tilting theory for such algebras. Under the assumption on existence of linear tilting (co)resolutions we show that algebras from this class are Koszul, that both the Ringel and Koszul duals belong to the same class, and that these two dualities on this class commute.

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n-T-COTORSION-FREE MODULES

Glasgow Mathematical Journal ◽

10.1017/s0017089519000107 ◽

2019 ◽

Vol 62 (2) ◽

pp. 297-311

Author(s):

DAJUN LIU ◽

JIAQUN WEI

Keyword(s):

Tilting Modules ◽

Tilting Theory ◽

Free Modules

AbstractIn order to better unify the tilting theory and the Auslander–Reiten theory, Xi introduced a general transpose called the relative transpose. Originating from this, we introduce and study the cotranspose of modules with respect to a left A-module T called n-T-cotorsion-free modules. Also, we give many properties and characteristics of n-T-cotorsion-free modules under the help of semi-Wakamatsu-tilting modules AT.

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