REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: The noncommutative torus A(t) is a universal C*-algebra on two generators u and v satisfying the unique relation vu= exp(it)uv for a real parameter t. It will be shown, that for each t the algebra A(t) is the natural coordinate ring for an elliptic curve over the complex numbers, i.e. isomorphic elliptic curves correspond to the stably isomorphic (Morita equivalent) noncommutative tori. Time permitting, some applications of this functor will be discussed. Reference: http://arxiv.org/abs/1109.6688