Let Λ be an Artin algebra. In this paper, the notion of $n\mathbb{Z}$-Gorenstein cluster tilting subcategories will be introduced. It is shown that every $n\mathbb{Z}$-cluster tilting subcategory of mod-Λ is $n\mathbb{Z}$-Gorenstein if and only if Λ is an Iwanaga-Gorenstein algebra. Moreover, it will be shown that an $n\mathbb{Z}$-Gorenstein cluster tilting subcategory of mod-Λ is an $n\mathbb{Z}$-cluster tilting subcategory of the exact category $\mathrm{Gprj}\text{-}\mathrm{\Lambda }$, the subcategory of all Gorenstein projective objects of mod-Λ. Some basic properties of $n\mathbb{Z}$-Gorenstein cluster tilting subcategories will be studied. In particular, we show that they are n-resolving, a higher version of resolving subcategories.

令Λ为Artin代数。在本文中，...的概念$ñ\mathbb{ž}$-将介绍Gorenstein群集倾斜子类别。结果表明，每$ñ\mathbb{ž}$-Λ的-集群倾斜子类别为 $ñ\mathbb{ž}$当且仅当Λ是Iwanaga-Gorenstein代数时，才使用-Gorenstein。而且，将显示出$ñ\mathbb{ž}$-mod-Λ的-Gorenstein簇倾斜子类别是 $ñ\mathbb{ž}$-确切类别的集群倾斜子类别 $\mathrm{Gprj}\text{--}\mathrm{\Lambda }$，是mod-Λ的所有Gorenstein射影对象的子类别。的一些基本特性$ñ\mathbb{ž}$-将研究Gorenstein群集倾斜子类别。特别是，我们表明它们是n-解析的，是解析子类别的更高版本。