Morita equivalence of multidimensional noncommutative tori

Abstract

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 $SO(n,n|\mathbf{Z})$ 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.

13 pages. Minor comment corrected. (To appear in the International Journal of Mathematics.)