Cluster characters II: a multiplication formula
| Autor: | Yann Palu |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Jussieu (IMJ), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2011 |
| Předmět: |
Path (topology)
Pure mathematics cluster algebras General Mathematics 18E30 16G20 Context (language use) 01 natural sciences Representation theory Cluster algebra Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Representation Theory (math.RT) 0101 mathematics Mathematics::Representation Theory Mathematics 2-Calabi--Yau triangulated categories [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT] Mathematics::Rings and Algebras 010102 general mathematics Quiver cluster characters Hall algebra 010307 mathematical physics Isomorphism Indecomposable module Mathematics - Representation Theory |
| Zdroj: | Proceedings of the London Mathematical Society. 104:57-78 |
| ISSN: | 0024-6115 |
| DOI: | 10.1112/plms/pdr027 |
| Popis: | Let $\mathcal{C}$ be a Hom-finite triangulated 2-Calabi-Yau category with a cluster tilting object. Under some constructibility assumptions on $\mathcal{C}$ which are satisfied for instance by cluster categories, by generalized cluster categories and by stable categories of modules over a preprojective algebra, we prove a multiplication formula for the cluster character associated with any cluster tilting object. This formula generalizes those obtained by Caldero-Keller for representation finite path algebras and by Xiao-Xu for finite-dimensional path algebras. It is analogous to a formula obtained by Geiss-Leclerc-Schr\"oer in the context of preprojective algebras. Comment: v3: Updated references. Section on Fu--Keller's cluster character. v4: Some expository changes as suggested by the referee. To appear in Proceedings LMS |
| Databáze: | OpenAIRE |
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