论文标题
半光，无扭转班和约旦 - 霍尔德财产
Semibricks, torsion-free classes and the Jordan-Hölder property
论文作者
论文摘要
令$ \ mathscr {c} $为外部类别，$ \ mathcal {x} $是$ \ Mathscr {C} $中的半核。令$ \ mathcal {t} $为$ \ Mathcal {x} $生成的过滤子类别。我们在$ \ Mathscr {C} $中介绍了弱的Jordan-Hölder财产（WJHP）和Jordan-Hölder属性（JHP），并显示$ \ Mathcal {t} $满意度（WJHP）。此外，当$ \ mathcal {t} $满足（JHP）时，并且仅当$ \ Mathcal {x} $正确。使用反射函数和$ c $ - 可容纳的元素，我们为$ a $ type $ a $ a $的表示类别提供了一个无扭矩满足（JHP）的组合标准。
Let $\mathscr{C}$ be an extriangulated category and $\mathcal{X}$ be a semibrick in $\mathscr{C}$. Let $\mathcal{T}$ be the filtration subcategory generated by $\mathcal{X}$. We introduce the weak Jordan-Hölder property (WJHP) and Jordan-Hölder property (JHP) in $\mathscr{C}$ and show that $\mathcal{T}$ satisfies (WJHP). Furthermore, $\mathcal{T}$ satisfies (JHP) if and only if $\mathcal{X}$ is proper. Using reflection functors and $c$-sortable elements, we give a combinatorial criterion for the torsion-free class satisfying (JHP) in the representation category of a quiver of type $A$.
