June 25, 2018

Ontario Non-Commutative Geometry Seminar

January 14, 2003-- 2:00 pm and January 28, 2003 --3:00 pm
Henrique Bursztyn, University of Toronto
Morita equivalence in (formal) deformation quantization

Roughly speaking, two algebras are Morita equivalent if they have equivalent "representation theories". This notion of equivalence plays a major role in noncommutative geometry, and also in applications of noncommutative geometry to physics.

In this talk, I will describe how to classify "quantum" algebras obtained by (formal) deformation quantization of Poisson manifolds up to Morita equivalence. This description involves, among other things, the study of projective modules over deformed algebras and deformation quantization of vector bundles.

If time permits, I will discuss strong Morita equivalence in the formal category, which is an algebraic generalization of Rieffel's
strong Morita equivalence of C*-algebras.

For more details on the thematic year, see Program Page