论文标题
Balmer Spectra和Drinfeld中心
Balmer spectra and Drinfeld centers
论文作者
论文摘要
单型三角类别的Balmer光谱是一种重要的几何结构，与对厚度张量理想进行分类密切相关。我们证明，来自有限张量类别的德林菲尔德中心的健忘函数$ {\ mathbf {c}} $ to $ {\ mathbf {c}} $扩展到其相应的稳定类别之间的单型三角函数，并在其balmer spectra之间连续映射。我们提供具有外观，过滤或同态性的条件。我们将这种一般理论应用于证明与有限维cosemisimple准hopf代数相关的Balmer光谱（尤其是在群体中的特征群中代数）与与Drinfeld双打相关的Balmer Spectra一致，并且两种类别的厚实的理想是生物的。对于某些Benson而言，类似的定理被证明是smash smash coproduct hopf代数，这些代数通常不是准文学。
The Balmer spectrum of a monoidal triangulated category is an important geometric construction which is closely related to the problem of classifying thick tensor ideals. We prove that the forgetful functor from the Drinfeld center of a finite tensor category ${\mathbf{C}}$ to ${\mathbf{C}}$ extends to a monoidal triangulated functor between their corresponding stable categories, and induces a continuous map between their Balmer spectra. We give conditions under which it is injective, surjective, or a homeomorphism. We apply this general theory to prove that Balmer spectra associated to finite-dimensional cosemisimple quasitriangular Hopf algebras (in particular, group algebras in characteristic dividing the order of the group) coincide with the Balmer spectra associated to their Drinfeld doubles, and that the thick ideals of both categories are in bijection. An analogous theorem is proven for certain Benson--Witherspoon smash coproduct Hopf algebras, which are not quasitriangular in general.
