Log-Modular Quantum Groups at Even Roots of Unity and the Quantum Frobenius I
Log-Modular Quantum Groups at Even Roots of Unity and the Quantum Frobenius I
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DOI：
10.1007/s00220-021-04012-2
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发表时间：
2018-12
影响因子：
2.4
通讯作者：
C. Negron
中科院分区：
文献类型：
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作者：
C. Negron
我们构造对数模量子群在偶数阶单位根，作为有限维带状准Hopf代数和有限带状张量范畴，通过de-equivarianization程序。这种量子群的存在已经被某些共形场论的考虑所预言，但直到最近才出现了结构。我们证明了我们的量子群在类型上可以与Creutzig-Gainutdinov-伦克尔量子群以及在任意Dynkin类型上与Gainutdinov-Lentner-Ohrmann量子群一致.讨论了顶点算子代数在（1，p）-中心荷上的拓扑关系.例如，我们解释了如何使用已知的三重顶点代数和量子之间的线性等价，结合我们的去等变结构提供的量子上的自然作用，以推导出“扩展”量子群，单重顶点算子代数和（1，p）-Virasoro对数最小模型之间的线性等价。我们假设在类型之外的单位根的阶上有一些限制，我们打算在随后的论文中消除这些限制。
We construct log-modular quantum groups at even order roots of unity, both as finite-dimensional ribbon quasi-Hopf algebras and as finite ribbon tensor categories, via a de-equivariantization procedure. The existence of such quantum groups had been predicted by certain conformal field theory considerations, but constructions had not appeared until recently. We show that our quantum groups can be identified with those of Creutzig-Gainutdinov-Runkel in type, and Gainutdinov-Lentner-Ohrmann in arbitrary Dynkin type. We discuss conjectural relations with vertex operator algebras at (1,p)-central charge. For example, we explain how one can (conjecturally) employ known linear equivalences between the triplet vertex algebra and quantum, in conjunction with a natural-action on quantumprovided by our de-equivariantization construction, in order to deduce linear equivalences between “extended” quantum groups, the singlet vertex operator algebra, and the (1,p)-Virasoro logarithmic minimal model. We assume some restrictions on the order of our root of unity outside of type, which we intend to eliminate in a subsequent paper.