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ICE-closed subcategories and epibricks over one-point extensions

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arxiv 2401.05645 v1 pith:JRHMU6YT submitted 2024-01-11 math.RT

classification math.RT
keywords ice-closedsubcategoriesepibrickssomeeveryextendedmodulesnumber
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abstract

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 $\tau$-tilting modules of $B$ by wide $\tau$-tilting modules of $A$.

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  1. ICE-closed subcategories and epibricks over recollements

    math.RT 2025-02 conditional novelty 5.0 of 10

    Over a recollement of abelian categories, ICE-closed subcategories, epibricks and monobricks glue and reduce along the recollement, yielding a bijection for ICE-closed subcategories under a natural containment condition.

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