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arXiv · 2404.15800

The Grothendieck group of a triangulated category

Xiao-Wu Chen·Zhi-Wei Li·Xiaojin Zhang·Zhibing Zhao
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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.

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Xiao-Wu Chen, Zhi-Wei Li, Xiaojin Zhang, Zhibing Zhao. 2024-04-24. The Grothendieck group of a triangulated category. https://arxiv.org/abs/2404.15800

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