The Grothendieck group of a triangulated category
Representation Theory
2024-08-01 v3 Category Theory
Abstract
We give a direct proof of the following known result: the Grothendieck group of a triangulated category with a silting subcategory is isomorphic to the split Grothendieck group of the silting subcategory. Moreover, we obtain its cluster-tilting analogue.
Keywords
Cite
@article{arxiv.2404.15800,
title = {The Grothendieck group of a triangulated category},
author = {Xiao-Wu Chen and Zhi-Wei Li and Xiaojin Zhang and Zhibing Zhao},
journal= {arXiv preprint arXiv:2404.15800},
year = {2024}
}
Comments
added a new section to discuss the cluster-tilting analogue