Motivated by a problem raised by Varadarajan, we show basic results on super-manifolds and super Lie groups over a complete field of characteristic $\ne 2$, extensively using Hopf-algebraic techniques. The main results are two theorems. The first shows a category equivalence between super Lie groups and Harish-Chandra pairs. The result is applied especially to construct the Hopf super-algebra of all analytic representative functions on a super Lie group. The second main theorem constructs homogeneous super-manifolds, showing their remarkable (probably new) property.

中文翻译：

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应用于全域超李群的 Hopf 代数技术

受 Varadarajan 提出的问题的启发，我们在特征 $\ne 2$ 的完整域上展示了超流形和超李群的基本结果，广泛使用了 Hopf 代数技术。主要结果是两个定理。第一个显示了超级李群和 Harish-Chandra 对之间的类别等价。该结果特别适用于构造超李群上所有解析代表函数的Hopf超代数。第二个主要定理构造了齐次超流形，展示了它们非凡的（可能是新的）性质。