Morita equivalence classes for crossed product of rational rotation algebras

2025/05/26 by Sayan Chakraborty, Chakraborty, Sayan, Kundu, Pratik Kumar · 1 citation
Mathematics · Computer Science · #Advanced Topics in Algebra #Advanced Algebra and Logic #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2505.19869

Abstract

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 SL(2, 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.

Citations

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