From smooth dynamical twists to twistors of quantum groupoids
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908706313076736 |
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| author | Cheng, Jiahao Chen, Zhuo Qiao, Yu Xiang, Maosong |
| author_facet | Cheng, Jiahao Chen, Zhuo Qiao, Yu Xiang, Maosong |
| contents | Consider a Lie subalgebra $\mathfrak{l} \subset \mathfrak{g}$ and an $\mathfrak{l}$-invariant open submanifold $V \subset \mathfrak{l}^{\ast}$. We demonstrate that any smooth dynamical twist on $V$, valued in $U(\mathfrak{g}) \otimes U(\mathfrak{g})\llbracket \hbar \rrbracket$, establishes a twistor on the associated quantum groupoid when combined with the Gutt star product on the cotangent bundle $T^\ast L$ of a Lie group $L$ that integrates $\mathfrak{l}$. This result provides a framework for constructing equivariant star products from smooth dynamical twists on those Poisson homogeneous spaces arising from nondegenerate polarized Lie algebras, leveraging the structure of twistors of quantum groupoids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09039 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From smooth dynamical twists to twistors of quantum groupoids Cheng, Jiahao Chen, Zhuo Qiao, Yu Xiang, Maosong Quantum Algebra 17B37 81R50 53D55 53D17 Consider a Lie subalgebra $\mathfrak{l} \subset \mathfrak{g}$ and an $\mathfrak{l}$-invariant open submanifold $V \subset \mathfrak{l}^{\ast}$. We demonstrate that any smooth dynamical twist on $V$, valued in $U(\mathfrak{g}) \otimes U(\mathfrak{g})\llbracket \hbar \rrbracket$, establishes a twistor on the associated quantum groupoid when combined with the Gutt star product on the cotangent bundle $T^\ast L$ of a Lie group $L$ that integrates $\mathfrak{l}$. This result provides a framework for constructing equivariant star products from smooth dynamical twists on those Poisson homogeneous spaces arising from nondegenerate polarized Lie algebras, leveraging the structure of twistors of quantum groupoids. |
| title | From smooth dynamical twists to twistors of quantum groupoids |
| topic | Quantum Algebra 17B37 81R50 53D55 53D17 |
| url | https://arxiv.org/abs/2412.09039 |