有限量子群的Galois重构

On the classification of Galois objects for finite groups

We classify Galois objects for the dual of a group algebra of a finite group over an arbitrary field.

有限量子群胚的Galois作用

Galois actions by finite quantum groupoids

提出了一类双代数胚映射，证明了在量子群胚作用下，平衡深度2扩张表现为有限Galois扩张，即，有限双代数胚、弱双代数或弱霍普夫代数的作用。本文讨论了弱双代数的变形、半群元、弱霍普夫代数重构的唯一性以及可分域扩张的例子。

有限群的量子伽罗瓦理论

Quantum Galois theory for finite groups

证明了单顶点算子代数V的有限自同构群G的子群与V的包含G-不变量集V^G的顶点算子子代数之间的伽罗瓦对应。

Braided join comodule algebras of Galois objects

We construct the join of noncommutative Galois objects (quantum torsors) over a Hopf algebra H. To ensure that the join algebra enjoys the natural (diagonal) coaction of H, we braid the tensor product of the Galois objects. Then we show that this coaction is principal. Our examples are built from the noncommutative torus with the natural free action of the classical torus, and arbitrary anti-Drinfeld doubles of finite-dimensional Hopf algebras. The former yields a noncommutative deformation of a non-trivial torus bundle, and the latter a finite quantum covering.

具有相同character表的有限群、Drinfel'd代数和Galois代数

Finite groups with the same character tables, Drinfel'd algebras and Galois algebras

证明了有限群具有相同的复特征标表当且仅当群代数是Drinfel'd拟双代数的扭形式或当且仅当这些群上存在非结合双Galois代数.同时给出了Drinfel'd代数上的保类自同构和具有相同特征的置换表示的解释。

Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras

We define polynomial H-identities for comodule algebras over a Hopf algebra H and establish general properties for the corresponding T-ideals. In the case H is a Taft algebra or the Hopf algebra E(n), we exhibit a finite set of polynomial H-identities which distinguish the Galois objects over H up to isomorphism.