完全域上超李群的Hopf代数技巧
Hopf-algebraic techniques applied to super Lie groups over a complete field
摘要：
我们展示了关于特征$\ne 2$的完全域上的超流形和超李群的基本结果，广泛地使用了Hopf代数技巧。主要结果是两个定理。第一个主要定理证明了超李群与Harish-Chandra对之间的范畴等价性，特别适用于构造超李群上所有解析表示函数的Hopf超代数。第二部分利用一种新的Hopf-代数方法构造了齐次超流形，并证明了它们的显著性质。
英文摘要：
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 main theorem shows a category equivalence between super Lie groups and Harish-Chandra pairs, which is applied especially to construct the Hopf super-algebra of all analytic representative functions on a super Lie group. The second constructs homogeneous super-manifolds by a new Hopf-algebraic method, showing their remarkable property.
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