Tame Algebras Have Dense g-Vector Fans
| Autor: | Toshiya Yurikusa, Bernhard Keller, Pierre-Guy Plamondon |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | International Mathematics Research Notices. 2023:2701-2747 |
| ISSN: | 1687-0247 1073-7928 |
| DOI: | 10.1093/imrn/rnab105 |
| Popis: | The $\textbf{g}$-vector fan of a finite-dimensional algebra is a fan whose rays are the $\textbf{g}$-vectors of its two-term presilting objects. We prove that the $\textbf{g}$-vector fan of a tame algebra is dense. We then apply this result to obtain a near classification of quivers for which the closure of the cluster $\textbf{g}$-vector fan is dense or is a half-space, using the additive categorification of cluster algebras by means of Jacobian algebras. As another application, we prove that for quivers with potentials arising from once-punctured closed surfaces, the stability and cluster scattering diagrams only differ by wall-crossing functions on the walls contained in a separating hyperplane. The appendix is devoted to the construction of truncated twist functors and their adjoints. |
| Databáze: | OpenAIRE |
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