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PERIMETER INSTITUTE RECORDED SEMINAR ARCHIVE

PIRSA:C07002 - Introduction to Quantum Groups 1 - 2007PODCAST Subscribe to podcast

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.

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Collection URL: http://pirsa.org/C07002



Introduction to quantum groups 1
Speaker(s): Florian Koch
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 Wey... read more
Date: 18/01/2007 - 9:00 am

Introduction to quantum groups 2
Speaker(s): Florian Koch
Abstract: Hopf-Algebras and their Representations In order to consolidate the above motivation, we have to introduce Hopf-algebras on a mathematical footing. We define Hopf-algebras, discuss duality and especially we will have a closer look at the question why coproducts induce a multiplication on the dual a... read more
Date: 19/01/2007 - 9:00 am

Introduction to quantum groups 3
Speaker(s): Florian Koch
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 ... read more
Date: 22/01/2007 - 9:00 am

Introduction to quantum groups 4
Speaker(s): Florian Koch
Abstract: This is the central unit of the course - we quantize universal enveloping algebras and their duals. Central discussion is the fact that for the first type of Hopf-algebras the deformation of the coproduct is sufficient and for the second type it is the dual multiplication. This motivates the way qua... read more
Date: 25/01/2007 - 9:00 am

Introduction to quantum groups 5
Speaker(s): Florian Koch
Abstract: Quantum Groups in Physics. With the gained background we want to review known quantum groups that became relevant in physics. Especially q-Deformation, kappa-Poincare- and theta-Poincare-Algebras are discussed.
Date: 26/01/2007 - 9:00 am
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