PIRSA:07010029

Introduction to quantum groups 3

Koch, F. (2007). Introduction to quantum groups 3. Perimeter Institute. https://pirsa.org/07010029

Koch, Florian. Introduction to quantum groups 3. Perimeter Institute, Jan. 22, 2007, https://pirsa.org/07010029 

          @misc{ pirsa_PIRSA:07010029,
            doi = {},
            url = {https://pirsa.org/07010029},
            author = {Koch, Florian},
            keywords = {},
            language = {en},
            title = {Introduction to quantum groups 3},
            publisher = {Perimeter Institute},
            year = {2007},
            month = {jan},
            note = {PIRSA:07010029 see, \url{https://pirsa.org}}
          }

Florian Koch Ludwig-Maximilians-Universitiät München (LMU)

Collection
Talk Type Course

Abstract

Universal Enveloping Algebras and dual Algebras of Functions The two most relevant types of Hopf-algebras for applications in physics are discussed in this unit. Most central notion will be their duality and representation.
Motivation: From Quantum Mechanics to Quantum GroupsThe 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.