Morita equivalence is an important equivalence relation for algebras, based on comparing categories of representations. There is also a geometric version of Morita equivalence in the realm of Poisson geometry, based on the notion of "dual pairs". In this talk, we will discuss how deformation quantization provides a concrete link between Morita equivalence of Poisson structures and their quantum algebras.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/3639