scholarly journals QUANTUM GROUP Uq(SU( 1，1))，UNIVERSAL R MATRIX AND CASIMIR INVARIANT

1994 ◽  
Vol 43 (2) ◽  
pp. 169
Author(s):  
ZHANG YAO-ZHONG
Keyword(s):  
Quantum Group ◽  
R Matrix ◽  
Casimir Invariant

scholarly journals R matrix for generalized quantum group of type A

2021 ◽  
Vol 566 ◽  
pp. 309-341
Author(s):  
Jae-Hoon Kwon ◽  
Jeongwoo Yu
Keyword(s):  
Quantum Group ◽  
Type A ◽  
R Matrix

scholarly journals Multiparametric and Colored Extensions of the Quantum Group GLq(N) and the Yangian Algebra Y(glN) Through a Symmetry Transformation of the Yang–Baxter Equation

1997 ◽  
Vol 12 (05) ◽  
pp. 945-962 ◽  
Author(s):  
B. Basu-Mallick ◽  
P. Ramadevi ◽  
R. Jagannathan
Keyword(s):  
Hopf Algebra ◽  
Quantum Group ◽  
Spectral Parameter ◽  
General Relation ◽  
Symmetry Transformation ◽  
Baxter Equation ◽  
Color Parameter ◽  
R Matrix ◽  
General Symmetry ◽  
Yangian Algebra

Inspired by Reshetikhin's twisting procedure to obtain multiparametric extensions of a Hopf algebra, a general "symmetry transformation" of the "particle conserving" R-matrix is found such that the resulting multiparametric R-matrix, with a spectral parameter as well as a color parameter, is also a solution of the Yang–Baxter equation (YBE). The corresponding transformation of the quantum YBE reveals a new relation between the associated quantized algebra and its multiparametric deformation. As applications of this general relation to some particular cases, multiparametric and colored extensions of the quantum group GL q(N) and the Yangian algebra Y(glN) are investigated and their explicit realizations are also discussed. Possible interesting physical applications of such extended Yangian algebras are indicated.

scholarly journals REMARKS ON THE QUANTUM GROUP STRUCTURE OF THE RATIONAL c<1 CONFORMAL THEORIES

1991 ◽  
Vol 06 (27) ◽  
pp. 4859-4884 ◽  
Author(s):  
P. FURLAN ◽  
A. CH. GANCHEV ◽  
V.B. PETKOVA
Keyword(s):  
Quantum Group ◽  
Group Structure ◽  
Extended Formulation ◽  
Conformal Blocks ◽  
Fusion Rules ◽  
R Matrix ◽  
Linear Relations ◽  
Intermediate States

The rational c<1 theories are reconsidered beyond the space of BRST states, allowing for intermediate states not contained in the Kac table. The intertwining properties of the screening charges Qm and Qp−m are used to derive linear relations for the general conformal blocks. The fusion rules are recovered on BRST states, combining these relations with previously obtained identities for the fusion matrices, due to the corresponding [Formula: see text]-invariant operators. The extended formulation is applied to give meaning for qp=1 to the quantum group covariant conformal correlations initiated by Moore and Reshetikhin. The correlations are manifestly covariant under the action of the R matrix and in the diagonal case they coincide with the averages of the screened vertices, recently proposed by Gómez and Sierra.

scholarly journals QUANTUM GROUP SYMMETRY OF INTEGRABLE SYSTEMS WITH OR WITHOUT BOUNDARY

2002 ◽  
Vol 17 (25) ◽  
pp. 3649-3661 ◽  
Author(s):  
E. RAGOUCY
Keyword(s):  
Quantum Group ◽  
Integrable Systems ◽  
Integrable Hierarchies ◽  
Group Symmetry ◽  
Integrals Of Motion ◽  
R Matrix ◽  
Explicit Expressions

We present a construction of integrable hierarchies without or with boundary, starting from a single R-matrix, or equivalently from a ZF algebra. We give explicit expressions for the Hamiltonians and the integrals of motion of the hierarchy in term of the ZF algebra. In the case without boundary, the integrals of motion form a quantum group, while in the case with boundary they form a Hopf coideal subalgebra of the quantum group.

scholarly journals $$R$$ R -Matrix Realization of Two-Parameter Quantum Group $$U_{r,s}(\mathfrak {gl}_n)$$ U r , s ( gl n )

2014 ◽  
Vol 2 (3-4) ◽  
pp. 211-230 ◽  
Author(s):  
Naihuan Jing ◽  
Ming Liu
Keyword(s):  
Quantum Group ◽  
R Matrix ◽  
Two Parameter

Quantum Group Construction of Non-standard R-matrix for Yang-Baxter Equation

1991 ◽  
Vol 8 (10) ◽  
pp. 495-498
Author(s):  
Ge Molin ◽  
Sun Changpu ◽  
Xue Kang
Keyword(s):  
Quantum Group ◽  
Baxter Equation ◽  
R Matrix ◽  
Group Construction

THE INHOMOGENEOUS QUANTUM INVARIANCE GROUP OF q-DEFORMED BOSON ALGEBRA

2009 ◽  
Vol 24 (38) ◽  
pp. 3137-3142 ◽  
Author(s):  
AZMI ALI ALTINTAS ◽  
METIN ARIK ◽  
ALI SERDAR ARIKAN
Keyword(s):  
Quantum Group ◽  
Invariance Group ◽  
R Matrix ◽  
R Relation ◽  
Inhomogeneous Quantum

We investigate the inhomogeneous invariance group of the q-deformed boson algebra. We find the R-matrix which gives the noncommuting structure of the quantum group with RM1M2 = M2M1R relation.

THE QUANTUM GROUP REALIZATIONS OF 3-D CHERN–SIMONS THEORIES

1995 ◽  
Vol 10 (01) ◽  
pp. 39-49
Author(s):  
C. RAMÍREZ ◽  
L. F. URRUTIA
Keyword(s):  
Quantum Group ◽  
Deformation Parameter ◽  
Canonical Quantization ◽  
Classical Case ◽  
Quantum Algebra ◽  
Simons Theory ◽  
R Matrix ◽  
The One ◽  
Chern Simons ◽  
Chern Simons Theory

The algebra of the integrated connections and of their traces is considered in the one-genus sector of classical and quantum Chern–Simons theory. In the classical case this algebra is braid-like and although the corresponding Jacobi identities are satisfied, the associated r-matrix does not satisfy the classical Yang–Baxter equations. However, it turns out this algebra originates a "quantum" algebra SU (2)q given by its trace algebra. Canonical quantization of the above algebra is performed and a one-parameter expression for the operator ordering is considered. The same quantum algebra with a modified deformation parameter, nontrivially depending on ħ, is obtained.

scholarly journals FRAME FORMALISM FOR THE N-DIMENSIONAL QUANTUM EUCLIDEAN SPACES

2000 ◽  
Vol 14 (22n23) ◽  
pp. 2305-2314 ◽  
Author(s):  
B. L. CERCHIAI ◽  
J. MADORE ◽  
G. FIORE
Keyword(s):  
Euclidean Space ◽  
Quantum Group ◽  
Moving Frame ◽  
Matrix Formalism ◽  
Euclidean Spaces ◽  
R Matrix ◽  
Covariant Derivatives ◽  
Torsion Free

We sketch our application1of a non-commutative version of the Cartan "moving-frame" formalism to the quantum Euclidean space [Formula: see text]the space which is covariant under the action of the quantum group SOq(N). For each of the two covariant differential calculi over [Formula: see text] based on the R-matrix formalism, we summarize our construction of a frame, the dual inner derivations, a metric and two torsion-free almost metric compatible covariant derivatives with a vanishing curvature. To obtain these results we have developed a technique which fully exploits the quantum group covariance of [Formula: see text]. We first find a frame in the larger algebra [Formula: see text]. Then we define homomorphisms from [Formula: see text] to [Formula: see text] which we use to project this frame in [Formula: see text].

The Heisenberg Quantum Group H(1) q : R-Matrix and Non-Commutative Spaces

1991 ◽  
pp. 140-142
Author(s):  
E. Celeghini ◽  
R. Giachetti ◽  
E. Sorace ◽  
M. Tarlini
Keyword(s):  
Quantum Group ◽  
R Matrix
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