Introduction to quantum groups 1

          @misc{ scivideos_PIRSA:07010027,
            doi = {},
            url = {https://pirsa.org/07010027},
            author = {Koch, Florian},
            keywords = {},
            language = {en},
            title = {Introduction to quantum groups 1},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2007},
            month = {jan},
            note = {PIRSA:07010027 see, \url{https://scivideos.org/pirsa/07010027}}
          }
          

Abstract

Motivation: From Quantum Mechanics to Quantum Groups The notion of 'quantization' commonly used in textbooks of quantum mechanics has to be specified in order to turn it into a defined mathematical operation. We discuss that on the trails of Weyl's phase space deformation, i.e. we introduce the Weyl-Moyal starproduct and the deformation of Poisson-manifolds. Generalizing from this, we understand, why Hopf-algebras are the most genuine way to apply 'quantization' to various other algebraic objects - and why this has direct physical applications.