Pith. sign in

ICE-closed subcategories and epibricks over one-point extensions

1 Pith paper cite this work. Polarity classification is still indexing.

1 Pith paper citing it
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 $A$.

citation-role summary

background 1

citation-polarity summary

fields

math.RT 1

years

2025 1

verdicts

CONDITIONAL 1

roles

background 1

polarities

unclear 1

representative citing papers

ICE-closed subcategories and epibricks over recollements

math.RT · 2025-02-06 · conditional · novelty 5.0

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.

citing papers explorer

Showing 1 of 1 citing paper.

  • ICE-closed subcategories and epibricks over recollements math.RT · 2025-02-06 · conditional · none · ref 26 · internal anchor

    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.