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Morita equivalence of multidimensional noncommutative tori

Marc Rieffel·Albert Schwarz
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Abstract

One can describe an $n$-dimensional noncommutative torus by means of an antisymmetric $n\times n$-matrix $θ$. We construct an action of the group $SO(n,n|\bf Z)$ on the space of antisymmetric matrices and show that, generically, matrices belonging to the same orbit of this group give Morita equivalent tori. Some applications to physics are sketched.

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Marc Rieffel, Albert Schwarz. 1998-08-20. Morita equivalence of multidimensional noncommutative tori. https://arxiv.org/abs/math/9803057

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