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Relations for the Grothendieck groups of triangulated categories

โœ Scribed by Jie Xiao; Bin Zhu

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
132 KB
Volume
257
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

A class of triangulated categories with a finiteness condition is singled out. These triangulated categories have Auslander-Reiten triangles. It is proved that the relations of the Grothendieck group of a triangulated category in this class are generated by all Auslander-Reiten triangles. Moreover, the Auslander-Reiten quivers of certain triangulated categories in this class are described in terms of Dynkin diagrams.

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