In this paper we provide upper estimates for the global projective dimensions of smooth crossed products \(\mathscr {S}(G, A; \alpha )\) for \(G = \mathbb {R}\) and \(G = \mathbb {T}\) and a self-induced Fréchet–Arens–Michael algebra A. To do this, we provide a powerful generalization of methods which are used in the works of Ogneva and Helemskii.

中文翻译：

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光滑交叉产品的同质尺寸

在本文中，我们提供的平滑交叉产品的全球投影尺寸上估计\（\ mathscr {S}（G，A; \阿尔法）\）为\（G = \ mathbb {R} \）和\（G = \ mathbb【T} \）和一个自诱导Fréchet可-阿伦斯-迈克尔代数甲。为此，我们提供了Ogneva和Helemskii作品中使用的方法的强大概括。