A Module-Theoretic Interpretation of Schiffler's Expansion Formula

Thomas Brüstle; Jie Zhang

doi:10.1080/00927872.2011.629267

A Module-Theoretic Interpretation of Schiffler's Expansion Formula

Thomas Brüstle, Jie Zhang^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We give a module-theoretic interpretation of Schiffler's expansion formula which is defined combinatorially in terms of complete (Γ, γ)-paths in order to get the expansion of the cluster variables in the cluster algebra of a marked surface (S, M). Based on the geometric description of the indecomposable objects of the cluster category of the marked surface (S, M), we show the coincidence of Schiffler-Thomas' expansion formula and the cluster character defined by Palu.

Original language	English
Pages (from-to)	260-283
Number of pages	24
Journal	Communications in Algebra
Volume	41
Issue number	1
DOIs	https://doi.org/10.1080/00927872.2011.629267
Publication status	Published - Jan 2013
Externally published	Yes

Keywords

Cluster algebras
Cluster categories
Marked surfaces
Representations

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10.1080/00927872.2011.629267

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AB - We give a module-theoretic interpretation of Schiffler's expansion formula which is defined combinatorially in terms of complete (Γ, γ)-paths in order to get the expansion of the cluster variables in the cluster algebra of a marked surface (S, M). Based on the geometric description of the indecomposable objects of the cluster category of the marked surface (S, M), we show the coincidence of Schiffler-Thomas' expansion formula and the cluster character defined by Palu.

KW - Cluster algebras

KW - Cluster categories

KW - Marked surfaces

KW - Representations

UR - https://www.scopus.com/pages/publications/84872413736

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JO - Communications in Algebra

JF - Communications in Algebra

IS - 1

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A Module-Theoretic Interpretation of Schiffler's Expansion Formula

Abstract

Keywords

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