论文标题
支持$τ_n$ - 用对
Support $τ_n$-tilting pairs
论文作者
论文摘要
我们介绍了Adachi-iyama-Reiten的支持$τ$的更高版本，这是雅各布森 - 乔根森的最大$τ_n$ - rigid对的概括。令$ \ mathcal c $为$（n+2）$ - Angulated类别，带有$ n $ -suspension functor $σ^n $和opperman-thomas-thomas cluster tilting对象。我们表明，$ \ MATHCAL C $中的相对$ n $ rigid对象进行双期培养，$τ_n$ -rigid对在$ n $ -Abelian类别中$ \ MATHCAL C/{\ MATHCAL C/{\ rm ADD}σ^n t $，相对最大$ n $ n $ rigiD $ rigid of $ \ rigig \ mathcal coptift $ \ tust $ ustiake n in tust $ rig \ tust in intut in intut intut in intut in intut intut in intut tust intut in intut intut intut in intut。我们还表明，相对$ n $ - 自我 - 垂直对象与Maximal $τ_n$ -rigid对进行了培养。这些结果将$ \ Mathcal C $的工作推广为Jacobsen-Jørgensen撰写的$ 2N $ -CALABI-YAU，而Yang-Zhu的工作则为$ n = 1 $。
We introduce the higher version of the notion of Adachi-Iyama-Reiten's support $τ$-tilting pairs, which is a generalization of maximal $τ_n$-rigid pairs in the sense of Jacobsen-Jørgensen. Let $\mathcal C$ be an $(n+2)$-angulated category with an $n$-suspension functor $Σ^n$ and an Opperman-Thomas cluster tilting object. We show that relative $n$-rigid objects in $\mathcal C$ are in bijection with $τ_n$-rigid pairs in the $n$-abelian category $\mathcal C/{\rm add}Σ^n T$, and relative maximal $n$-rigid objects in $\mathcal C$ are in bijection with support $τ_n$-tilting pairs. We also show that relative $n$-self-perpendicular objects are in bijection with maximal $τ_n$-rigid pairs. These results generalise the work for $\mathcal C$ being $2n$-Calabi-Yau by Jacobsen-Jørgensen and the work for $n=1$ by Yang-Zhu.
