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Article Dans Une Revue International Mathematics Research Notices Année : 2023

Tame Algebras Have Dense g-Vector Fans

Résumé

The g-vector fan of a finite-dimensional algebra is a fan whose rays are the g-vectors of its two-term presilting objects. We prove that the 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 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.
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Dates et versions

hal-04122823 , version 1 (08-02-2024)

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Pierre Guy Plamondon, T. Yurikusa, B. Keller. Tame Algebras Have Dense g-Vector Fans. International Mathematics Research Notices, 2023, 2023 (4), pp.2701-2747. ⟨10.1093/imrn/rnab105⟩. ⟨hal-04122823⟩
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