Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.20661 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909805758644224 |
|---|---|
| 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 |