Morita equivalence classes for crossed product of rational rotation algebras
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915335006846976 |
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| author | Chakraborty, Sayan Kundu, Pratik Kumar |
| author_facet | Chakraborty, Sayan Kundu, Pratik Kumar |
| contents | We study the Morita equivalence classes of crossed products of rotation algebras $A_θ$, where $θ$ is a rational number, by finite and infinite cyclic subgroups of $\mathrm{SL}(2, \mathbb{Z})$. We show that for any such subgroup $F$, the crossed products $A_θ\rtimes F$ and $A_{θ'} \rtimes F$ are strongly Morita equivalent, where both $θ$ and $θ'$ are rational. Combined with previous results for irrational values of $θ$, our result provides a complete classification of the crossed products $A_θ\rtimes F$ up to Morita equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19869 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Morita equivalence classes for crossed product of rational rotation algebras Chakraborty, Sayan Kundu, Pratik Kumar Operator Algebras 46L35, 46L55 We study the Morita equivalence classes of crossed products of rotation algebras $A_θ$, where $θ$ is a rational number, by finite and infinite cyclic subgroups of $\mathrm{SL}(2, \mathbb{Z})$. We show that for any such subgroup $F$, the crossed products $A_θ\rtimes F$ and $A_{θ'} \rtimes F$ are strongly Morita equivalent, where both $θ$ and $θ'$ are rational. Combined with previous results for irrational values of $θ$, our result provides a complete classification of the crossed products $A_θ\rtimes F$ up to Morita equivalence. |
| title | Morita equivalence classes for crossed product of rational rotation algebras |
| topic | Operator Algebras 46L35, 46L55 |
| url | https://arxiv.org/abs/2505.19869 |