Morita equivalence of smooth noncommutative tori

Abstract

We show that in the generic case the smooth noncommutative tori associated to two n by n real skew-symmetric matrices are Morita equivalent if and only if the matrices are in the same orbit of the natural SO(n, n| Z) action.

27 pages. Final version. To appear in Acta Math

References in corpus (4)

• Introduction to M(atrix) theory and noncommutative geometry, Part II
• Introduction to M(atrix) theory and noncommutative geometry
• Crossed products by finite cyclic group actions with the tracial Rokhlin property
• The noncommutative geometry of the discrete Heisenberg group