论文标题
可逆编织张量类别
Invertible braided tensor categories
论文作者
论文摘要
我们证明，在Morita 4类Brtens中，有限的编织张量类别A在编织的张量类别中是可逆的，并且只有当它是非分类的。这包括半神经模块化张量类别的情况，但还包括非偏simimple的示例，例如良好根源的小量子组的表示类别。通过COBORDISM假设，我们获得了新的可逆的4维框架拓扑领域理论，我们认为这是在半岛案例中自由使用和Walker的构造之后的Crane-Yetter-Kauffman不变性的非偏式框架版本。更笼统地，我们表征了任意对称的单体OO类别中E_1-和E_2- algebras的可逆性，并且我们猜想对任何N的可逆E_N-Algebras具有类似的表征。最后，我们提出了Brtens的Picard小组，作为Witt构成的非统治融合类别的概括，并提出了许多关于它的开放问题。
We prove that a finite braided tensor category A is invertible in the Morita 4-category BrTens of braided tensor categories if, and only if, it is non-degenerate. This includes the case of semisimple modular tensor categories, but also non-semisimple examples such as categories of representations of the small quantum group at good roots of unity. Via the cobordism hypothesis, we obtain new invertible 4-dimensional framed topological field theories, which we regard as a non-semisimple framed version of the Crane-Yetter-Kauffman invariants, after Freed--Teleman and Walker's construction in the semisimple case. More generally, we characterize invertibility for E_1- and E_2-algebras in an arbitrary symmetric monoidal oo-category, and we conjecture a similar characterization of invertible E_n-algebras for any n. Finally, we propose the Picard group of BrTens as a generalization of the Witt group of non-degenerate braided fusion categories, and pose a number of open questions about it.
