On Gauge Equivalence of Twisted Quantum Doubles
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910645889269760 |
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| author | Li, Bowen Liu, Gongxiang |
| author_facet | Li, Bowen Liu, Gongxiang |
| contents | 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 $D_8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09353 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Gauge Equivalence of Twisted Quantum Doubles Li, Bowen Liu, Gongxiang Quantum Algebra Rings and Algebras 16T05, 17B37, 18M20 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 $D_8$. |
| title | On Gauge Equivalence of Twisted Quantum Doubles |
| topic | Quantum Algebra Rings and Algebras 16T05, 17B37, 18M20 |
| url | https://arxiv.org/abs/2408.09353 |