论文标题
纤维函子的单一转换
Unitary transformations of fibre functors
论文作者
论文摘要
我们研究纤维函子prep（g） - > hilb之间的统一假性变换（UPTS），其中g是紧凑型量子组。对于纤维函子F_1，F_2我们表明UPTS F_1-> f_2的类别和修改对相应的BI-HOPF-GALOIS对象的有限维 *的类别是同构。我们从Canonical Fiber函子以及UPT本身可以访问Frobenius代数REP（A_G）中，从而使UPT访问纤维函子的建设性分类，其中A_G是a_g是hopf *-ergebra dual dual to to compact compact量子组。例如，我们表明，来自量子图X的有限维量子同构是在REP（G_X）上的纤维函子之间的UPT，其中G_X是X的量子自动形态组。
We study unitary pseudonatural transformations (UPTs) between fibre functors Rep(G) -> Hilb, where G is a compact quantum group. For fibre functors F_1, F_2 we show that the category of UPTs F_1 -> F_2 and modifications is isomorphic to the category of finite-dimensional *-representations of the corresponding bi-Hopf-Galois object. We give a constructive classification of fibre functors accessible by a UPT from the canonical fibre functor, as well as UPTs themselves, in terms of Frobenius algebras in the category Rep(A_G), where A_G is the Hopf *-algebra dual to the compact quantum group. As an example, we show that finite-dimensional quantum isomorphisms from a quantum graph X are UPTs between fibre functors on Rep(G_X), where G_X is the quantum automorphism group of X.
