Mathematics

In this talk I will present the construction and some properties for the Kasprzak approach to Quantization Deformation, also called Cocycle Deformation. This construction can be considered as a far generalization of the Rieffel pseudo-differential calculus. While the Rieffel construction is done using hard elements of analysis, the new approach suggests to consider the crossed product construction and Duality Theorems for C^*-algebras, getting a more algebraic approach with possible generalizations to more general situations.  As an application, I will show how it can be used to define quantizations of certain Poisson structures.