Quivers with relations for symmetrizable Cartan matrices V. Caldero-Chapoton formula
| Autor: | Geiß, Christof, Leclerc, Bernard, Schröer, Jan |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Proc. Lond. Math. Soc. (3) 117 (2018), no. 1, 125-148 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/plms.12146 |
| Popis: | We generalize the Caldero-Chapoton formula for cluster algebras of finite type to the skew-symmetrizable case. This is done by replacing representation categories of Dynkin quivers by categories of locally free modules over certain Iwanaga-Gorenstein algebras introduced in Part I. The proof relies on the realization of the positive part of the enveloping algebra of a simple Lie algebra of the same finite type as a convolution algebra of constructible functions on representation varieties of $H$, given in Part III. Along the way, we obtain a new result on the PBW basis of this convolution algebra. Comment: 24 pages. V2: Exposition improved and a few typos fixed after referee report. Final version, to appear in Proc. London Math. Soc |
| Databáze: | arXiv |
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