论文标题
定期三角类别中的倾斜对象
Tilting objects in periodic triangulated categories
论文作者
论文摘要
悬浮函数$σ$满足$σ^m \ simeq \ mathrm {id} _ {\ mathcal {t}} $作为加性函数的$σ^m \ simeq \ mathrm {iD} _ $σ^m \ simeq \ mathrm {这样的类别没有周期性的倾斜对象。 In this paper, we introduce the notion of an $m$-periodic tilting object in an $m$-periodic triangulated category, which is a periodic analogue of a tilting object in a triangulated category, and prove that an $m$-periodic triangulated category having an $m$-periodic tilting object is triangulated equivalent to the $m$-periodic derived category在某些同源假设下的代数。作为一个应用程序，我们在自注射代数的稳定类别与遗传代数的$ m $ $ $ periodic派生类别之间构建了三角构剖分的对等。
A triangulated category $\mathcal{T}$ whose suspension functor $Σ$ satisfies $Σ^m \simeq \mathrm{Id}_{\mathcal{T}}$ as additive functors is called an $m$-periodic triangulated category. Such a category does not have a tilting object by the periodicity. In this paper, we introduce the notion of an $m$-periodic tilting object in an $m$-periodic triangulated category, which is a periodic analogue of a tilting object in a triangulated category, and prove that an $m$-periodic triangulated category having an $m$-periodic tilting object is triangulated equivalent to the $m$-periodic derived category of an algebra under some homological assumptions. As an application, we construct a triangulated equivalence between the stable category of a self-injective algebra and the $m$-periodic derived category of a hereditary algebra.
