Speaker: Hanfeng Li,
Institution: Univeristy of Toronto,
Title:
Morita equivalence of higher dimensional noncommutative tori
Date: Friday, Jan. 24,
Time: 4-5pm
Place: Milner 317
Abstract:
Morita equivalent C*-algebras share many important properties
(e.g. isomorphic K-groups, cyclic homology, etc). For every
antisymmetric n by n matrix one can associate an n-dimensional
noncommutative torus, which is one of the classical examples in
Noncommutative Differential Geometry. In 1998 Rieffel and Schwarz
constructed an action of the group SO(n,n|Z) on the space of n by n
antisymmetric matrices and showed that, generically, matrices belonging to
the same orbit of this group give Morita equivalent tori. They also
conjectured that this is always true instead of only "generically".
We prove their conjecture.