度量Tannakian对偶
Metric Tannakian Duality
摘要：
我们将度量数据的Tannaka-Krein对偶的框架。因此，对于任何具有左不变度量的群，我们在它的酉表示范畴上产生一个对偶度量。我们的特点的条件下，一个“双对偶”度量的组可以恢复从度量的表示，并提供条件下，一个度量同意其双对偶。我们还考虑了T-对偶和量子Gromov-Hausdorff距离的一些应用。
英文摘要：
We incorporate metric data into the framework of Tannaka-Krein duality. Thus, for any group with left invariant metric, we produce a dual metric on its category of unitary representations. We characterize the conditions under which a "double-dual" metric on the group may be recovered from the metric on representations, and provide conditions under which a metric agrees with its double-dual. We also consider some applications to T-duality and quantum Gromov-Hausdorff distance.
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