Hopf Algebras and q-Deformation Quantum Groups

2006 ◽  
pp. 687-700
Author(s):  
S. Majid
Keyword(s):  
Quantum Groups ◽  
Hopf Algebras

scholarly journals INTRODUCTION TO QUANTIZED LIE GROUPS AND ALGEBRAS

1992 ◽  
Vol 07 (25) ◽  
pp. 6175-6213 ◽  
Author(s):  
T. TJIN
Keyword(s):  
Lie Groups ◽  
Quantum Groups ◽  
Hopf Algebras ◽  
Baxter Equation ◽  
Product Decomposition ◽  
R Matrix ◽  
Conformal Field ◽  
Finite Dimensional ◽  
Lie Groups And Algebras ◽  
Poisson Lie Groups

We give a self-contained 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 representation theory. Introductions to Hopf algebras, Poisson structures and deformation quantization are also provided. After defining Poisson Lie groups we study their relation to Lie bialgebras and the classical Yang-Baxter equation. Then we explain in detail the concept of quantization for them. As an example the quantization of sl2 is explicitly carried out. Next we show how quantum groups are related to the Yang-Baxter equation and how they can be used to solve it. Using the quantum double construction we explicitly construct the universal R matrix for the quantum sl2 algebra. In the last section we deduce all finite-dimensional irreducible representations for q a root of unity. We also give their tensor product decomposition (fusion rules), which is relevant to conformal field theory.

scholarly journals Multi-brace cotensor Hopf algebras and quantum groups

2016 ◽  
Vol 286 (1-2) ◽  
pp. 657-678
Author(s):  
Xin Fang ◽  
Marc Rosso
Keyword(s):  
Quantum Groups ◽  
Hopf Algebras

scholarly journals Quantum groups and conformal field theories

1989 ◽  
Vol 329 (1605) ◽  
pp. 343-347
Keyword(s):  
Hopf Algebra ◽  
Quantum Groups ◽  
Hopf Algebras ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Theory ◽  
Conformal Field

Rational conformal field theories can be interpreted as defining quasi-triangular Hopf algebras. The Hopf algebra is determined by the duality properties of the conformal theory.

scholarly journals Differential Hopf Algebras on Quantum Groups of Type A

1999 ◽  
Vol 214 (2) ◽  
pp. 479-518 ◽  
Author(s):  
Axel Schüler
Keyword(s):  
Quantum Groups ◽  
Hopf Algebras ◽  
Type A

Complex Quantum Groups and Their Dual Hopf Algebras

1992 ◽  
pp. 13-22 ◽  
Author(s):  
Bernhard Drabant ◽  
Michael Schlieker ◽  
Wolfgang Weich ◽  
Bruno Zumino
Keyword(s):  
Quantum Groups ◽  
Hopf Algebras

scholarly journals A class of C∗-algebraic locally compact quantum groupoids part I. Motivation and definition

2018 ◽  
Vol 29 (04) ◽  
pp. 1850029 ◽  
Author(s):  
Byung-Jay Kahng ◽  
Alfons Van Daele
Keyword(s):  
Quantum Groups ◽  
Hopf Algebras ◽  
Idempotent Element ◽  
Locally Compact ◽  
Locally Compact Quantum Groups ◽  
Multiplier Hopf Algebras ◽  
Compact Quantum Groups

In this series of papers, we develop the theory of a class of locally compact quantum groupoids, which is motivated by the purely algebraic notion of weak multiplier Hopf algebras. In this Part I, we provide motivation and formulate the definition in the [Formula: see text]-algebra framework. Existence of a certain canonical idempotent element is required and it plays a fundamental role, including the establishment of the coassociativity of the comultiplication. This class contains locally compact quantum groups as a subclass.

Sign in / Sign up

Export Citation Format

Share Document