An Imprimitivity Theorem for finite algebraic quantum groups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913585674846208 |
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| author | Ellis, Eugenia González, Ana Tartaglia, Gisela |
| author_facet | Ellis, Eugenia González, Ana Tartaglia, Gisela |
| contents | Let $\mathcal{G}$ be an algebraic quantum group and $\mathcal{U}$ a compact quantum subgroup. Given a left $\hat{\mathcal{U}}$-module algebra A with unit, we can endow $A\otimes\mathcal{G}$ with a structure of a right $\hat{\mathcal{U}}$-module algebra. The algebra of invariants for this action $(A\otimes\mathcal{G})^{\hat{\mathcal{U}}}$ has a left action of $\hat{\mathcal{G}}$. We prove that for finite $\mathcal{G}$, $(A\otimes\mathcal{G})^{\hat{\mathcal{U}}}\#\hat{\mathcal{G}}$ is Morita equivalent to $A\#\hat{\mathcal{U}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11501 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Imprimitivity Theorem for finite algebraic quantum groups Ellis, Eugenia González, Ana Tartaglia, Gisela Quantum Algebra 16T05, 16T20 Let $\mathcal{G}$ be an algebraic quantum group and $\mathcal{U}$ a compact quantum subgroup. Given a left $\hat{\mathcal{U}}$-module algebra A with unit, we can endow $A\otimes\mathcal{G}$ with a structure of a right $\hat{\mathcal{U}}$-module algebra. The algebra of invariants for this action $(A\otimes\mathcal{G})^{\hat{\mathcal{U}}}$ has a left action of $\hat{\mathcal{G}}$. We prove that for finite $\mathcal{G}$, $(A\otimes\mathcal{G})^{\hat{\mathcal{U}}}\#\hat{\mathcal{G}}$ is Morita equivalent to $A\#\hat{\mathcal{U}}$. |
| title | An Imprimitivity Theorem for finite algebraic quantum groups |
| topic | Quantum Algebra 16T05, 16T20 |
| url | https://arxiv.org/abs/2401.11501 |