The Grothendieck groups of n-cluster categories of type A_{\infty}
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909805758644224 |
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| author | Chang, Huimin |
| author_facet | Chang, Huimin |
| contents | In this article, we investigate the Grothendieck groups $K_0(\C_{A_{\infty}}^n)$ of $n$-cluster categories $\C_{A_{\infty}}^n$ of type $A_{\infty}$ introduced by T.~Holm and P.~Jørgensen. We prove that $K_0(\C_{A_{\infty}}^n)\cong\mathbb{Z}$ for an arbitrary $n\geq 1$. As an application, this generalizes a result of Murphy for $n=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20661 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Grothendieck groups of n-cluster categories of type A_{\infty} Chang, Huimin Representation Theory In this article, we investigate the Grothendieck groups $K_0(\C_{A_{\infty}}^n)$ of $n$-cluster categories $\C_{A_{\infty}}^n$ of type $A_{\infty}$ introduced by T.~Holm and P.~Jørgensen. We prove that $K_0(\C_{A_{\infty}}^n)\cong\mathbb{Z}$ for an arbitrary $n\geq 1$. As an application, this generalizes a result of Murphy for $n=1$. |
| title | The Grothendieck groups of n-cluster categories of type A_{\infty} |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2509.20661 |