论文标题
Tambara-Yamagami，Loop Groups，Bundles和KK理论
Tambara-Yamagami, loop groups, bundles and KK-theory
论文作者
论文摘要
本文是序列解释的序列的一部分，从理论上讲述了共形场理论k。在这里，我们提供了相关模块类别（模块化不变，Nimreps等）的几何结构。特别是，我们对tori循环组以及最著名的循环组模块化群体对所有模块化不变性提供了KK理论的解释。此外，我们出乎意料地发现，tambara-yamagami融合类别在群体上具有优雅的描述，并用它来将其模块类别解释为KK元素。我们为所有Tambara-Yamagami类别的双打建立重建，将Bischoff的工作概括为偶数群体。最后，我们将来自有限群体和循环组的模块化组表示与Chern角色以及傅立叶 - 穆凯变换有关
This paper is part of a sequence interpreting quantities of conformal field theories K-theoretically. Here we give geometric constructions of the associated module categories (modular invariants, nimreps, etc). In particular, we give a KK-theory interpretation of all modular invariants for the loop groups of tori, as well as most known modular invariants of loop groups. In addition, we find unexpectedly that the Tambara-Yamagami fusion category has an elegant description as bundles over a groupoid, and use that to interpret its module categories as KK-elements. We establish reconstruction for the doubles of all Tambara-Yamagami categories, generalizing work of Bischoff to even-order groups. We conclude by relating the modular group representations coming from finite groups and loop groups to the Chern character and to the Fourier-Mukai transform
