Morita equivalence of multidimensional noncommutative tori
- Author(s): Rieffel, Marc;
- Schwarz, Albert
- et al.
Published Web Locationhttps://arxiv.org/pdf/math/9803057.pdf
One can describe an $n$-dimensional noncommutative torus by means of an antisymmetric $n\times n$-matrix $\theta$. 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.