Relations for the Grothendieck groups of triangulated categories
type: Item
instance of: scholarly article
title: Relations for the Grothendieck groups of triangulated categories
zbMATH Open document ID: 1021.18004
DOI: 10.1016/S0021-8693(02)00122-9
author: Jie Xiao
author: Bin Zhu
published in: Journal of Algebra
publication date: 2003-02-12T00:00:00Z
review text: The authors study the relations of the Grothendieck groups of triangulated categories of finite type by using the Auslander-Reiten triangle as well as the Auslander-Reiten quivers of triangulated categories of finite type. It is proved that the relations of the Grothendieck group of triangulated categories of finite type are generated by all Auslander-Reiten triangles. Also, it is shown that if there is no loop in the Auslander-Reiten quiver of a triangulated category of finite type then it can be described in terms of Dynkin diagrams. Some special triangulated categories without loops in its Auslander-Reiten quivers are presented.
reviewed by: Constantin Năstăsescu
Mathematics Subject Classification ID: 18E30
zbMATH DE Number: 1868053
zbMATH Keywords: triangulated category of finite type
zbMATH Keywords: Grothendieck group
zbMATH Keywords: Auslander-Reiten triangle
zbMATH Keywords: Auslander-Reiten quivers
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1868053