Grothendieck groups and Auslander-Reiten (d+2)-angles

JOURNAL OF ALGEBRA

卷:568

Article

Zhou, Panyue¹ 

[1] Hunan Inst Sci & Technol, Coll Math, Yueyang 414006, Hunan, Peoples R China

关键词: (d+2)-angulated categories;    Auslander-Reiten (d+2)-angles;    Locally finite;    Triangulated categories;    Grothendieck groups;   

DOI  :  10.1016/j.jalgebra.2020.09.048

来源: Elsevier

【 摘 要 】

Xiao and Zhu have shown that if C is a locally finite triangulated category, then the Auslander-Reiten triangles generate the relations for the Grothendieck group of C. The notion of (d+2)-angulated categories is a higher dimensional analogue of triangulated categories. In this article, we show that a (d + 2)-angulated category C with d odd is locally finite if and only if the Auslander-Reiten (d+2)-angles generate the relations for the Grothendieck group of C. This extends the result of Xiao and Zhu, and gives the converse of Xiao and Zhu's result is also true. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free