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arXiv · 2107.13482

Acyclic cluster algebras with dense $g$-vector fans

Toshiya Yurikusa
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Abstract

The $g$-vector fans play an important role in studying cluster algebras and silting theory. We survey cluster algebras with dense $g$-vector fans and show that a connected acyclic cluster algebra has a dense $g$-vector fan if and only if it is either finite type or affine type. As an application, we classify finite dimensional hereditary algebras with dense $g$-vector fans.

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BibTeXRIS

Toshiya Yurikusa. 2021-07-28. Acyclic cluster algebras with dense $g$-vector fans. https://doi.org/10.2969/aspm%2F08810437

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