Silting and tilting objects in cleft extensions of abelian categories
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915784028061696 |
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| author | Zhao, Guoqiang Sun, Juxiang |
| author_facet | Zhao, Guoqiang Sun, Juxiang |
| contents | We establish connections between silting and tilting objects in an abelian category $\mathcal{B}$ and those in a cleft extension $\mathcal{A}$ of $\mathcal{B}$, which provides a method for constructing more silting and tilting objects. Then we apply our results to the cleft extensions of module categories, and characterize silting and tilting modules over $θ$-extension of rings. Some known results over trivial extension of rings are extended and strengthened. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07368 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Silting and tilting objects in cleft extensions of abelian categories Zhao, Guoqiang Sun, Juxiang Representation Theory 16D90, 16G10, 18G10, 18G25 We establish connections between silting and tilting objects in an abelian category $\mathcal{B}$ and those in a cleft extension $\mathcal{A}$ of $\mathcal{B}$, which provides a method for constructing more silting and tilting objects. Then we apply our results to the cleft extensions of module categories, and characterize silting and tilting modules over $θ$-extension of rings. Some known results over trivial extension of rings are extended and strengthened. |
| title | Silting and tilting objects in cleft extensions of abelian categories |
| topic | Representation Theory 16D90, 16G10, 18G10, 18G25 |
| url | https://arxiv.org/abs/2602.07368 |