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 $C$ to $C$ 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.

幺半群三角范畴的巴尔默谱是一种重要的几何构造，与厚张量理想的分类问题密切相关。我们证明了来自有限张量范畴的 Drinfeld 中心的健忘函子$C$到$C$扩展到它们相应的稳定类别之间的幺半群三角函子，并在它们的巴尔默谱之间产生连续的映射。我们给出它是单射、满射或同胚的条件。我们应用这个一般理论来证明与有限维余半单拟三角 Hopf 代数（特别是划分群阶的特征群代数）相关的巴尔默谱与与它们的德林菲尔德双打相关的巴尔默谱一致，并且厚理想两个类别都是双射的。对于某些 Benson-Witherspoon 粉碎余积 Hopf 代数，可以证明类似的定理，这些代数通常不是拟三角形的。