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arXiv · 2505.19869

Morita equivalence classes for crossed product of rational rotation algebras

Sayan Chakraborty·Pratik Kumar Kundu
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Abstract

We study the Morita equivalence classes of crossed products of rotation algebras $A_\theta$, where $\theta$ 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 $A_\theta \rtimes F$ and $A_{\theta'} \rtimes F$ are strongly Morita equivalent, where both $\theta$ and $\theta'$ are rational. Combined with previous results for irrational values of $\theta$, our result provides a complete classification of the crossed products $A_\theta \rtimes F$ up to Morita equivalence.

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Sayan Chakraborty, Pratik Kumar Kundu. 2025-05-26. Morita equivalence classes for crossed product of rational rotation algebras. https://arxiv.org/abs/2505.19869

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