Illinois Journal of Mathematics

On tilting modules over cluster-tilted algebras

David Smith

Full-text: Open access

Abstract

In this paper, we show that the tilting modules over a cluster-tilted algebra $A$ lift to tilting objects in the associated cluster category $\mathcal{C}_H$. As a first application, we describe the induced exchange relation for tilting $A$-modules arising from the exchange relation for tilting object in $\mathcal{C}_H$. As a second application, we exhibit tilting $A$-modules having cluster-tilted endomorphism algebras.

Article information

Source
Illinois J. Math., Volume 52, Number 4 (2008), 1223-1247.

Dates
First available in Project Euclid: 18 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258554359

Digital Object Identifier
doi:10.1215/ijm/1258554359

Mathematical Reviews number (MathSciNet)
MR2595764

Zentralblatt MATH identifier
1204.16009

Subjects
Primary: 16G20: Representations of quivers and partially ordered sets 18E30: Derived categories, triangulated categories

Citation

Smith, David. On tilting modules over cluster-tilted algebras. Illinois J. Math. 52 (2008), no. 4, 1223--1247. doi:10.1215/ijm/1258554359. https://projecteuclid.org/euclid.ijm/1258554359


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