R-matrix approach to differential calculus on quantum groups

1997 ◽  
Vol 28 (3) ◽  
pp. 267 ◽  
Author(s):  
A. P. Isaev
Keyword(s):  
Quantum Groups ◽  
Differential Calculus ◽  
Matrix Approach ◽  
R Matrix

scholarly journals Uq(N) GAUGE THEORIES

1994 ◽  
Vol 09 (30) ◽  
pp. 2835-2847 ◽  
Author(s):  
LEONARDO CASTELLANI
Keyword(s):  
Quantum Groups ◽  
Differential Calculus ◽  
Gauge Theories ◽  
Space Time ◽  
Yang Mills ◽  
Commutation Relations ◽  
Transformation Rules ◽  
Field Strengths

Improving on an earlier proposal, we construct the gauge theories of the quantum groups U q(N). We find that these theories are also consistent with an ordinary (commuting) space-time. The bicovariance conditions of the quantum differential calculus are essential in our construction. The gauge potentials and the field strengths are q-commuting "fields," and satisfy q-commutation relations with the gauge parameters. The transformation rules of the potentials generalize the ordinary infinitesimal gauge variations. For particular deformations of U (N) ("minimal deformations"), the algebra of quantum gauge variations is shown to close, provided the gauge parameters satisfy appropriate q-commutations. The q-Lagrangian invariant under the U q(N) variations has the Yang–Mills form [Formula: see text], the "quantum metric" gij being a generalization of the Killing metric.

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.

An R-matrix approach to the quantization of the Euclidean group E(2)

1993 ◽  
Vol 26 (24) ◽  
pp. 7495-7501 ◽  
Author(s):  
A Ballesteros ◽  
E Celeghini ◽  
R Giachetti ◽  
E Sorace ◽  
M Tarlini
Keyword(s):  
Matrix Approach ◽  
Euclidean Group ◽  
R Matrix

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
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