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 WeylMoyal starproduct and the deformation of Poissonmanifolds. Generalizing from this, we understand, why Hopfalgebras 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
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
Collection: Introduction to Quantum Groups 1  2007

Introduction to quantum groups 2 Speaker(s): Florian Koch
Abstract: HopfAlgebras and their Representations
In order to consolidate the above motivation, we have to introduce Hopfalgebras on a mathematical footing. We define Hopfalgebras, 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
Collection: Introduction to Quantum Groups 1  2007

Introduction to quantum groups 3 Speaker(s): Florian Koch
Abstract: Universal Enveloping Algebras and dual Algebras of Functions
The two most relevant types of Hopfalgebras 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 'quantiz... read more
Date: 22/01/2007  9:00 am
Collection: Introduction to Quantum Groups 1  2007

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 Hopfalgebras 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
Collection: Introduction to Quantum Groups 1  2007

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 qDeformation, kappaPoincare and thetaPoincareAlgebras are discussed.
Date: 26/01/2007  9:00 am
Collection: Introduction to Quantum Groups 1  2007
