Morita equivalence classes for crossed product of rational rotation algebras

Fuente: arXiv
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Autori principali: Chakraborty, Sayan, Kundu, Pratik Kumar
Natura: Preprint
Pubblicazione: 2025
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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