VOL. 88 | 2023 Acyclic cluster algebras with dense $g$-vector fans
Toshiya Yurikusa

Editor(s) Yukari Ito, Akira Ishii, Osamu Iyama

Adv. Stud. Pure Math., 2023: 437-459 (2023) DOI: 10.2969/aspm/08810437

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.

Information

Published: 1 January 2023
First available in Project Euclid: 8 May 2023

Digital Object Identifier: 10.2969/aspm/08810437

Subjects:
Primary: 05E45 , 13F60 , 16G20

Keywords: $g$-vector fan , 2-term silting theory , cluster algebra

Rights: Copyright © 2023 Mathematical Society of Japan

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