ICE-closed subcategories and epibricks over one-point extensions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917563811758080 |
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| author | Li, Xin Gao, Hanpeng |
| author_facet | Li, Xin Gao, Hanpeng |
| contents | Let $B$ be the one-point extension algebra of $A$ by an $A$-module $M$. We proved that every ICE-closed subcategory in$\mod A$ can be extended to be some ICE-closed subcategories in$\mod B$.In the same way, every epibrick in $\mod A$ can be extended to be some epibricks in $\mod B$.The number of ICE-closed subcategories in $\mod B$ and the number of ICE-closed subcategories in $\mod A$ are denoted respectively as $m$, $n$.We can conclude the following inequality:$$m \geq 2n$$ This is the analogical in epibricks.As an application, we can get some wide $τ$-tilting modules of $B$ by wide $τ$-tilting modules of $A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05645 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | ICE-closed subcategories and epibricks over one-point extensions Li, Xin Gao, Hanpeng Representation Theory 16G20 Let $B$ be the one-point extension algebra of $A$ by an $A$-module $M$. We proved that every ICE-closed subcategory in$\mod A$ can be extended to be some ICE-closed subcategories in$\mod B$.In the same way, every epibrick in $\mod A$ can be extended to be some epibricks in $\mod B$.The number of ICE-closed subcategories in $\mod B$ and the number of ICE-closed subcategories in $\mod A$ are denoted respectively as $m$, $n$.We can conclude the following inequality:$$m \geq 2n$$ This is the analogical in epibricks.As an application, we can get some wide $τ$-tilting modules of $B$ by wide $τ$-tilting modules of $A$. |
| title | ICE-closed subcategories and epibricks over one-point extensions |
| topic | Representation Theory 16G20 |
| url | https://arxiv.org/abs/2401.05645 |