Smooth group representations on bornological vector spaces
Smooth group representations on bornological vector spaces
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DOI：
10.1016/j.bulsci.2003.12.002
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发表时间：
2003-10
影响因子：
1.3
通讯作者：
R. Meyer
中科院分区：
文献类型：
--
作者：
R. Meyer
我们发展了边界向量空间上局部紧群的光滑表示的基本理论。在这种情况下，我们能够建立比在拓扑情况下更好的一般定理。尽管如此，向量空间上完全不连通群和Fréchet空间上李群的光滑表示仍然是我们理论的特例。我们在适当的卷积代数上用本质模来识别光滑表示。我们考察了表示和模上的光滑函子，并证明了如果它们都被定义，则它们是一致的。我们利用伴随函子技巧建立了诱导函子和紧诱导函子的基本性质。我们描述了光滑表示范畴的中心。
We develop the basic theory of smooth representations of locally compact groups on bornological vector spaces. In this setup, we are able to formulate better general theorems than in the topological case. Nonetheless, smooth representations of totally disconnected groups on vector spaces and of Lie groups on Fréchet spaces remain special cases of our theory. We identify smooth representations with essential modules over an appropriate convolution algebra. We examine smoothening functors on representations and modules and show that they agree if they are both defined. We establish the basic properties of induction and compact induction functors using adjoint functor techniques. We describe the center of the category of smooth representations.