scholarly journals COMMENT ON THE DIFFERENTIAL CALCULUS ON THE QUANTUM EXTERIOR PLANE

1998 ◽  
Vol 13 (20) ◽  
pp. 1645-1651 ◽  
Author(s):  
SALIH ÇELIK ◽  
SULTAN A. ÇELIK ◽  
METIN ARIK
Keyword(s):  
Symmetry Group ◽  
Differential Calculus ◽  
Baxter Equation ◽  
Oscillator Algebra ◽  
Quantum Deformation ◽  
R Matrix ◽  
Two Parameter ◽  
Parameter Deformation

We give a two-parameter quantum deformation of the exterior plane and its differential calculus without the use of any R-matrix and relate it to the differential calculus with the R-matrix. We prove that there are two types of solutions of the Yang–Baxter equation whose symmetry group is GL p,q(2). We also give a two-parameter deformation of the fermionic oscillator algebra.

COVARIANT DIFFERENTIAL CALCULI ON QUANTUM SYMPLECTIC AND ORTHOGONAL PLANES

1993 ◽  
Vol 08 (05) ◽  
pp. 389-397
Author(s):  
PREETI PARASHAR ◽  
V.S. BHASIN ◽  
S.K. SONI
Keyword(s):  
Differential Calculus ◽  
Baxter Equation ◽  
R Matrix ◽  
Consistency Conditions

We study covariant differential calculi on quantum symplectic and orthogonal planes as interesting examples of the Wess-Zumino formalism for general non-(anti-)commutative differential calculus on quantum planes. The aim of this exercise is to generate certain known R-matrix solutions of the quantum Yang-Baxter equation. This is achieved by treating the consistency conditions on the calculus in a manner different from that of Wess and Zumino.

scholarly journals QUASI THREE-PARAMETRIC R-MATRIX AND QUANTUM SUPERGROUPS GLp,q(1/1) AND Up,q[gl(1/1)]

2019 ◽  
Vol 29 (4) ◽  
pp. 511
Author(s):  
Nguyen Thi Hong Van ◽  
Nguyen Anh Ky
Keyword(s):  
Universal Enveloping Algebra ◽  
Present Approach ◽  
Baxter Equation ◽  
Quantum Deformation ◽  
R Matrix ◽  
Enveloping Algebra ◽  
Quantum Deformations ◽  
First Time

An overparametrized (three-parametric) R-matrix satisfying a graded Yang-Baxter equation is introduced. It turns out that such an overparametrization is very helpful. Indeed, this R-matrix with one of the parameters being auxiliary, thus, reducible to a two-parametric R-matrix, allows the construction of quantum supergroups GLp,q(1/1) and Up,q[gl(1/1)] which, respectively, are two-parametric deformations of the supergroup GL(1/1) and the universal enveloping algebra U[gl(1/1)]. These two-parametric quantum deformations GLpq(1/1) and Upq[gl(1/1)], to our knowledge, are constructed for the first time via the present approach. The quantum deformation Up,q[gl(1/1)] obtained here is a true two-parametric deformation of Drinfel’d-Jimbo’s type, unlike some other one obtained previously elsewhere.

scholarly journals TWO-PARAMETER QUANTUM-DEFORMED DUAL AMPLITUDE

1995 ◽  
Vol 10 (01) ◽  
pp. 51-60 ◽  
Author(s):  
L. JENKOVSZKY ◽  
M. KIBLER ◽  
A. MISHCHENKO
Keyword(s):  
Harmonic Oscillator ◽  
Oscillator Algebra ◽  
Dual Amplitude ◽  
Two Parameter ◽  
Dual Models ◽  
Parameter Deformation

A four-point dual amplitude, with nonlinear trajectories, is constructed from a two-parameter deformation of the harmonic oscillator algebra. The earlier versions of the q-deformed dual models are reproduced as limiting cases of the model introduced in the present work.

scholarly journals Degenerate Sklyanin algebras

Open Physics ◽  
2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Andrey Smirnov
Keyword(s):  
Difference Operators ◽  
Baxter Equation ◽  
Quantum Algebras ◽  
Rational Solutions ◽  
R Matrix ◽  
Gauge Transformations ◽  
Sklyanin Algebras ◽  
Sklyanin Algebra ◽  
The Difference

AbstractNew trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl(N;?)-case is discussed.

scholarly journals A Two-Parameter Quantum Deformation of the Unit Disc

1993 ◽  
Vol 115 (1) ◽  
pp. 1-23 ◽  
Author(s):  
S. Klimek ◽  
A. Lesniewski
Keyword(s):  
Unit Disc ◽  
Quantum Deformation ◽  
Two Parameter
Sign in / Sign up

Export Citation Format

Share Document