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PIRSA:07010029

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https://pirsa.org/07010029

Introduction to quantum groups 3

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

Florian Koch Ludwig-Maximilians-Universitiät München (LMU)

Talk numberPIRSA:07010029
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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.