关于扭曲量子双的规范等价性
On Gauge Equivalence of Twisted Quantum Doubles
AI总结：
本文研究了3-上圈扭曲的有限阿贝尔群量子双的规范等价条件，并应用于余根分次有限维余拟Hopf代数的分类及Nichols代数的无限维性证明。
摘要：
我们研究了由3-上圈扭曲的有限阿贝尔群G的量子双，并给出了此类扭曲量子双与有限群的普通量子双规范等价的充分条件。此外，我们确定了循环群的扭曲量子双何时是真正的。作为应用，我们为阿贝尔群上余根分次的有限维余拟Hopf代数的分类做出了贡献。作为副产品，我们证明了Nichols代数$\mathcal{B}(M_1\oplus M_2 \oplus M_3)$是无限维的，其中$M_1,M_2,M_3$是$D_8$的三个不同的单Yetter-Drinfeld模。
英文摘要：
We study the quantum double of a finite abelian group $G$ twisted by a $3$-cocycle and give a sufficient condition when such a twisted quantum double will be gauge equivalent to a ordinary quantum double of a finite group. Moreover, we will determine when a twisted quantum double of a cyclic group is genuine. As an application, we contribute to the classification of coradically graded finite-dimensional pointed coquasi-Hopf algebras over abelian groups. As a byproduct, we show that the Nichols algebras $\mathcal{B}(M_1\oplus M_2 \oplus M_3)$ are infinite-dimensional where $M_1,M_2,M_3$ are three different simple Yetter-Drinfeld modules of $D_8$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
