$nd\mathbb{Z}$-cluster tilting subcategories of $d$-Nakayama algebras
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917400981536768 |
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| author | Xing, Wei |
| author_facet | Xing, Wei |
| contents | Jasso-Külshammer introduced the class of $d$-Nakayama algebras as a higher dimensional analogue of Nakayama algebras. In particular, they are endowed with a distinguished $d\mathbb{Z}$-cluster tilting subcategory. In this paper, we investigate which $d$-Nakayama algebras admit an $nd\mathbb{Z}$-cluster tilting subcategory for $n>1$. The radical square zero case is already covered by results on classical Nakayama algebras due to Herschend-Kvamme-Vaso. For each remaining non-self-injective $d$-Nakayama algebra, we provide a complete classification of its $nd\mathbb{Z}$-cluster tilting subcategories. In fact, there exists at most one for a suitable integer $n$. A self-injective $d$-Nakayama algebra is determined by two positive integers $m$ and $l$. We show that an $nd\mathbb{Z}$-cluster tilting subcategory is only possible if $n|m$ and $n|(l-2)$. In case $n=l-2$, we show that such subcategory does indeed exist by constructing an explicit example. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_28236 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $nd\mathbb{Z}$-cluster tilting subcategories of $d$-Nakayama algebras Xing, Wei Representation Theory 16G20, 16E65 Jasso-Külshammer introduced the class of $d$-Nakayama algebras as a higher dimensional analogue of Nakayama algebras. In particular, they are endowed with a distinguished $d\mathbb{Z}$-cluster tilting subcategory. In this paper, we investigate which $d$-Nakayama algebras admit an $nd\mathbb{Z}$-cluster tilting subcategory for $n>1$. The radical square zero case is already covered by results on classical Nakayama algebras due to Herschend-Kvamme-Vaso. For each remaining non-self-injective $d$-Nakayama algebra, we provide a complete classification of its $nd\mathbb{Z}$-cluster tilting subcategories. In fact, there exists at most one for a suitable integer $n$. A self-injective $d$-Nakayama algebra is determined by two positive integers $m$ and $l$. We show that an $nd\mathbb{Z}$-cluster tilting subcategory is only possible if $n|m$ and $n|(l-2)$. In case $n=l-2$, we show that such subcategory does indeed exist by constructing an explicit example. |
| title | $nd\mathbb{Z}$-cluster tilting subcategories of $d$-Nakayama algebras |
| topic | Representation Theory 16G20, 16E65 |
| url | https://arxiv.org/abs/2603.28236 |