Cocycle twisting of semidirect products and transmutation
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916095712034816 |
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| author | Habbestad, Erik Neshveyev, Sergey |
| author_facet | Habbestad, Erik Neshveyev, Sergey |
| contents | We apply Majid's transmutation procedure to Hopf algebra maps $H \to \mathbb C[T]$, where $T$ is a compact abelian group, and explain how this construction gives rise to braided Hopf algebras over quotients of $T$ by subgroups that are cocentral in $H$. This allows us to unify and generalize a number of recent constructions of braided compact quantum groups, starting from the braided $SU_q(2)$ quantum group, and describe their bosonizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00494 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cocycle twisting of semidirect products and transmutation Habbestad, Erik Neshveyev, Sergey Quantum Algebra Operator Algebras We apply Majid's transmutation procedure to Hopf algebra maps $H \to \mathbb C[T]$, where $T$ is a compact abelian group, and explain how this construction gives rise to braided Hopf algebras over quotients of $T$ by subgroups that are cocentral in $H$. This allows us to unify and generalize a number of recent constructions of braided compact quantum groups, starting from the braided $SU_q(2)$ quantum group, and describe their bosonizations. |
| title | Cocycle twisting of semidirect products and transmutation |
| topic | Quantum Algebra Operator Algebras |
| url | https://arxiv.org/abs/2304.00494 |