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arXiv · 0710.4329

On tilting modules over cluster-tilted algebras

David Smith
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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.

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David Smith. 2007-10-23. On tilting modules over cluster-tilted algebras. https://arxiv.org/abs/0710.4329

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