On endomorphism algebras of silting complexes over hereditary abelian categories
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918382866006016 |
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| author | Dai, Wei Fu, Changjian Peng, Liangang |
| author_facet | Dai, Wei Fu, Changjian Peng, Liangang |
| contents | Let $\mathcal{E}$ be the class of finite-dimensional algebras isomorphic to endomorphism algebras of silting complexes over hereditary abelian categories. It is proved that the class $\mathcal{E}$ is closed under taking idempotent quotients, idempotent subalgebras and $τ$-reduction. We also show that the proper class consisting of shod algebras is also closed under these operations. In addition, several classic classes of algebras -- including laura, glued, weakly shod algebras -- are proved to be closed under idempotent quotients, thereby generalizing a known result originally established for specific idempotents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17197 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On endomorphism algebras of silting complexes over hereditary abelian categories Dai, Wei Fu, Changjian Peng, Liangang Representation Theory 16G10, 16E10, 18E30 Let $\mathcal{E}$ be the class of finite-dimensional algebras isomorphic to endomorphism algebras of silting complexes over hereditary abelian categories. It is proved that the class $\mathcal{E}$ is closed under taking idempotent quotients, idempotent subalgebras and $τ$-reduction. We also show that the proper class consisting of shod algebras is also closed under these operations. In addition, several classic classes of algebras -- including laura, glued, weakly shod algebras -- are proved to be closed under idempotent quotients, thereby generalizing a known result originally established for specific idempotents. |
| title | On endomorphism algebras of silting complexes over hereditary abelian categories |
| topic | Representation Theory 16G10, 16E10, 18E30 |
| url | https://arxiv.org/abs/2602.17197 |