Replicated algebras derived equivalent to higher Auslander algebras of type A
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918221459750912 |
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| author | Xing, Wei |
| author_facet | Xing, Wei |
| contents | We show that every higher Auslander algebra $A_{n+1}^d$ of type $\mathbb{A}$ such that $\gcd(n,d)=1$ is derived equivalent to a certain replicated algebra $B=B_0^{(n+d)}$. Moreover ${\rm{gldim}} B = nd$ and $B$ admits an $nd$-cluster tilting subcategory consisting of all direct sums of projective modules and injective modules. We introduce a class of algebras called $2$-subhomogeneous $m$-representation finite to characterize the homological properties of $B$ and give a method to obtain derived equivalences between fractionally Calabi-Yau algebras and $2$-subhomogeneous algebras using certain tilting complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22655 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Replicated algebras derived equivalent to higher Auslander algebras of type A Xing, Wei Representation Theory 16G20, 16E65 We show that every higher Auslander algebra $A_{n+1}^d$ of type $\mathbb{A}$ such that $\gcd(n,d)=1$ is derived equivalent to a certain replicated algebra $B=B_0^{(n+d)}$. Moreover ${\rm{gldim}} B = nd$ and $B$ admits an $nd$-cluster tilting subcategory consisting of all direct sums of projective modules and injective modules. We introduce a class of algebras called $2$-subhomogeneous $m$-representation finite to characterize the homological properties of $B$ and give a method to obtain derived equivalences between fractionally Calabi-Yau algebras and $2$-subhomogeneous algebras using certain tilting complexes. |
| title | Replicated algebras derived equivalent to higher Auslander algebras of type A |
| topic | Representation Theory 16G20, 16E65 |
| url | https://arxiv.org/abs/2511.22655 |