PIRSA:C07002 - Introduction to Quantum Groups 1
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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.
Organizer(s):
Collection URL: http://pirsa.org/C07002
Introduction to quantum groups 1
Speaker(s):
Florian Koch - Institute for Theoretical Physics at the University of Munich. Germany.
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 moreDate: 18/01/2007 - 9:00 am
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Introduction to quantum groups 2
Speaker(s):
Florian Koch - Institute for Theoretical Physics at the University of Munich. Germany.
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 moreDate: 19/01/2007 - 9:00 am
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Introduction to quantum groups 3
Speaker(s):
Florian Koch - Institute for Theoretical Physics at the University of Munich. Germany.
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.
Date: 22/01/2007 - 9:00 am
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Introduction to quantum groups 4
Speaker(s):
Florian Koch - Institute for Theoretical Physics at the University of Munich. Germany.
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 moreDate: 25/01/2007 - 9:00 am
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Introduction to quantum groups 5
Speaker(s):
Florian Koch - Institute for Theoretical Physics at the University of Munich. Germany.
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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