Abstract This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures from a noncommutative embedding space to a noncommutative hypersurface is developed and applied to obtain noncommutative hypersurface Dirac operators. The general construction is illustrated by studying the sequence T θ 2 ↪ S θ 3 ↪ R θ 4 of noncommutative hypersurface embeddings.

中文翻译：

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非对易超曲面上的狄拉克算子

摘要 本文在非对易黎曼（自旋）几何的模理论方法中研究了非对易超曲面上的几何结构。开发了从非对易嵌入空间到非对易超曲面诱导微分、黎曼和旋涡结构的构造，并应用于获得非对易超曲面狄拉克算子。通过研究非交换超曲面嵌入的序列 T θ 2 ↪ S θ 3 ↪ R θ 4 来说明一般构造。