scholarly journals Geometrical Meaning of R -Matrix Action for Quantum Groups at Roots of 1

1997 ◽  
Vol 184 (1) ◽  
pp. 95-117 ◽  
Author(s):  
Fabio Gavarini
Keyword(s):  
Quantum Groups ◽  
Geometrical Meaning ◽  
R Matrix

scholarly journals R-matrix and Mickelsson algebras for orthosymplectic quantum groups

2015 ◽  
Vol 56 (8) ◽  
pp. 081701 ◽  
Author(s):  
Thomas Ashton ◽  
Andrey Mudrov
Keyword(s):  
Quantum Groups ◽  
R Matrix

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.

R-matrix method for Heisenberg quantum groups

1994 ◽  
Vol 31 (2) ◽  
pp. 159-166 ◽  
Author(s):  
V. Hussin ◽  
A. Lauzon ◽  
G. Rideau
Keyword(s):  
Quantum Groups ◽  
Matrix Method ◽  
R Matrix

Universal R-matrix and representation theory for quantum groups

1992 ◽  
Vol 164 (5-6) ◽  
pp. 389-397 ◽  
Author(s):  
V.Ya. Chernyak ◽  
K.I. Grigorishin ◽  
E.I. Ogievetsky
Keyword(s):  
Representation Theory ◽  
Quantum Groups ◽  
R Matrix

scholarly journals Two-parameter Quantum Groups of Exceptional Type E-Series and Convex PBW-type Basis

2008 ◽  
Vol 15 (04) ◽  
pp. 619-636 ◽  
Author(s):  
Xiaotang Bai ◽  
Naihong Hu
Keyword(s):  
Quantum Groups ◽  
Quantum Double ◽  
R Matrix ◽  
Double Structure ◽  
The One ◽  
Two Parameter

The presentation of two-parameter quantum groups of type E-series in the sense of Benkart–Witherspoon is given, which has a Drinfel'd quantum double structure. The universal R-matrix and a convex PBW-type basis are described for type E6(as a sample), and the conditions of an isomorphism from these quantum groups into the one-parameter quantum doubles are discussed.

scholarly journals Universal R-matrix and functional relations

2014 ◽  
Vol 26 (06) ◽  
pp. 1430005 ◽  
Author(s):  
Herman Boos ◽  
Frank Göhmann ◽  
Andreas Klümper ◽  
Khazret S. Nirov ◽  
Alexander V. Razumov
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Integrable Systems ◽  
Vertex Model ◽  
Quantum Space ◽  
R Matrix ◽  
Functional Relations

We collect and systematize general definitions and facts on the application of quantum groups to the construction of functional relations in the theory of integrable systems. As an example, we reconsider the case of the quantum group [Formula: see text] related to the six-vertex model. We prove the full set of the functional relations in the form independent of the representation of the quantum group in the quantum space and specialize them to the case of the six-vertex model.

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