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Title: Physics/Quantum Mechanics - An introduction to Quantized Lie Groups and Algebras We give a selfcontained introduction to the theory of quantum groups according to Drinfeld highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representat
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[hep-th/9111043] An introduction to quantized Lie groups and algebras

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High Energy Physics - Theory

Title:An introduction to quantized Lie groups and algebras

Authors:T.Tjin(Submitted on 21 Nov 1991 (v1), last revised 26 Nov 1991 (this version, v2))Abstract: We give a selfcontained introduction to the theory of quantum groupsaccording to Drinfeld highlighting the formal aspects as well as theapplications to the Yang-Baxter equation and representation theory.Introductions to Hopf algebras, Poisson structures and deformation quantizationare also provided. After having defined Poisson-Lie groups we study theirrelation to Lie-bi algebras and the classical Yang-Baxter equation. Then weexplain in detail the concept of quantization for them. As an example thequantization of $sl_2$ is explicitly carried out. Next we show how quantumgroups are related to the Yang-Baxter equation and how they can be used tosolve it. Using the quantum double construction we explicitly construct theuniversal $R$-matrix for the quantum $sl_2$ algebra. In the last section wededuce all finite dimensional irreducible representations for $q$ a root ofunity. We also give their tensor product decomposition (fusion rules) which isrelevant to conformal field theory.Comments:38 pagesSubjects:High Energy Physics - Theory (hep-th)Journal reference:Int.J.Mod.Phys. A7 (1992) 6175-6213Cite as:arXiv:hep-th/9111043v2

Submission history

From: Tjark Tjin [view email][v1] Thu, 21 Nov 1991 14:18:58 GMT (0kb,I)[v2] Tue, 26 Nov 1991 13:24:09 GMT (29kb)Which authors of this paper are endorsers?Link back to: arXiv, form interface, contact.
 

We

give

a

selfcontained

introduction

to

the

theory

of

quantum

groups

according

to

Drinfeld

highlighting

the

formal

aspects

as

well

as

the

applications

to

the

Yang-Baxter

equation

and

representat

http://arxiv.org/abs/hep-th/9111043

An introduction to Quantized Lie Groups and Algebras 2008 November

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We give a selfcontained introduction to the theory of quantum groups according to Drinfeld highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representat

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