Morita equivalence of multidimensional noncommutative tori

Details Morita equivalence of multidimensional noncommutative tori Morita equivalence of multidimensional noncommutative tori

1998-03-13

arxiv.org/abs/math/9803057v4

Int.J.Math. 10 (1999) 289-299

Mathematics

Quantum Algebra

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

Scientific paper

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.

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