Triangle equivalences between Gorenstein tiled orders and incidence algebras of posets
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918319073787904 |
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| author | Iyama, Osamu Liu, Junyang |
| author_facet | Iyama, Osamu Liu, Junyang |
| contents | We prove that for any $\mathbb{N}$-graded Gorenstein tiled order $A$, the stable category $\underline{\mathrm{CM}}^{\mathbb{Z}}A$ is triangle equivalent to the perfect derived category of the incidence algebra of a finite poset $\mathbb{V}_A^{op}$. Moreover, for a finite poset $P$, we prove that the incidence algebra of $P$ can be realized as the endomorphism algebra of a standard tilting object if and only if $P$ is either empty or has the maximum. We also study the behaviors of the corresponding poset under graded Morita equivalences and coverings of a Gorenstein tiled order. Finally, we classify Gorenstein tiled orders $A$ satisfying $|\mathbb{V}_A^{op}|\leq 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01878 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Triangle equivalences between Gorenstein tiled orders and incidence algebras of posets Iyama, Osamu Liu, Junyang Representation Theory Commutative Algebra Combinatorics Rings and Algebras 18G80, 18G65, 16G50, 16G20 We prove that for any $\mathbb{N}$-graded Gorenstein tiled order $A$, the stable category $\underline{\mathrm{CM}}^{\mathbb{Z}}A$ is triangle equivalent to the perfect derived category of the incidence algebra of a finite poset $\mathbb{V}_A^{op}$. Moreover, for a finite poset $P$, we prove that the incidence algebra of $P$ can be realized as the endomorphism algebra of a standard tilting object if and only if $P$ is either empty or has the maximum. We also study the behaviors of the corresponding poset under graded Morita equivalences and coverings of a Gorenstein tiled order. Finally, we classify Gorenstein tiled orders $A$ satisfying $|\mathbb{V}_A^{op}|\leq 3$. |
| title | Triangle equivalences between Gorenstein tiled orders and incidence algebras of posets |
| topic | Representation Theory Commutative Algebra Combinatorics Rings and Algebras 18G80, 18G65, 16G50, 16G20 |
| url | https://arxiv.org/abs/2602.01878 |