一类方便的超流形
A convenient category of supermanifolds
摘要：
为了在有限维李群的无限维表示理论中的应用，我们引入了一类新的超流形。在这一范畴中，存在“映射”和“场”（纤维丛截面）的超流形。特别是，循环超群可以在这个框架中实现全球。它还为超群的诱导表示提供了一个方便的设置，允许一个版本的弗罗贝纽斯互惠。最后，引入有限维李超群的卷积代数，并证明了一个超群Dixmier-Malliavin定理：超群对的连续表示的光滑向量空间等于由紧支撑光滑超群密度的卷积所给出的Garding空间.
英文摘要：
With a view towards applications in the theory of infinite-dimensional representations of finite-dimensional Lie supergroups, we introduce a new category of supermanifolds. In this category, supermanifolds of `maps' and `fields' (fibre bundle sections) exist. In particular, loop supergroups can be realised globally in this framework. It also provides a convenient setting for induced representations of supergroups, allowing for a version of Frobenius reciprocity. Finally, convolution algebras of finite-dimensional Lie supergroups are introduced and applied to a prove a supergroup Dixmier-Malliavin Theorem: The space of smooth vectors of a continuous representation of a supergroup pair equals the Garding space given by the convolution with compactly supported smooth supergroup densities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
