30 nov 2016 -- 14:30
Sala Riunioni, Dipartimento di Matematica, Università degli Studi di Salerno
Abstract.
In the 1980's Vladimir Drinfel'd introduced the notion of twist which led to a special kind of deformation quantization of a physical system via its symmetries. The advantage of this approach is that one is not only quantizing the system but also its symmetries and any module algebra of the symmetries in a compatible way. In this seminar we define the basic algebraic structures that are needed to encode symmetries, their interaction with the physical system and the twist. Further, we want to embed this algebraic picture in the context of Poisson geometry. Finally, we give examples of twist deformation quantization but also obstructions, namely on the symplectic 2-sphere and the higher genus Riemann surfaces.