Acyclic cluster algebras with dense $g$-vector fans

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.

23 pages

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Cited by in corpus (2)

• Denseness of $g$-vector cones from weighted orbifolds
• Unbounded ${\mathfrak{sl}}_3$-laminations and their shear coordinates