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 JORDANIAN QUANTUM SUPERALGEBRA Uh(osp(2/1))

2003 ◽  
Vol 18 (13) ◽  
pp. 885-903 ◽  
Author(s):  
N. AIZAWA ◽  
R. CHAKRABARTI ◽  
J. SEGAR
Keyword(s):  
Algebraic Structure ◽  
Lie Superalgebra ◽  
Universal Enveloping Algebra ◽  
Borel Subalgebra ◽  
Quantum Deformation ◽  
R Matrix ◽  
Enveloping Algebra ◽  
Quantum Superalgebra ◽  
Tensor Operators

A quantum deformation of the Lie superalgebra osp(2/1) from the classical r-matrix including an odd generator is presented with its full Hopf algebraic structure. A class of deformation maps and the corresponding twisting elements, the interrelation between these twists, and the tensor operators are considered for the deformed osp(2/1) algebra. It is also shown that the Borel subalgebra of the universal enveloping algebra of the quantized osp(2/1) is self-dual.

scholarly journals A TRIANGULAR DEFORMATION OF THE TWO-DIMENSIONAL POINCARÉ ALGEBRA

1995 ◽  
Vol 10 (11) ◽  
pp. 873-883 ◽  
Author(s):  
M. KHORRAMI ◽  
A. SHARIATI ◽  
M.R. ABOLHASSANI ◽  
A. AGHAMOHAMMADI
Keyword(s):  
Hopf Algebra ◽  
Lorentz Transformation ◽  
Hopf Algebras ◽  
Universal Enveloping Algebra ◽  
Two Dimensional ◽  
R Matrix ◽  
Enveloping Algebra ◽  
Differential Structure ◽  
Algebra Of Functions ◽  
Poincaré Algebra

Contracting the h-deformation of SL(2, ℝ), we construct a new deformation of two-dimensional Poincaré's algebra, the algebra of functions on its group and its differential structure. It is seen that these dual Hopf algebras are isomorphic to each other. It is also shown that the Hopf algebra is triangular, and its universal R-matrix is also constructed explicitly. We then find a deformation map for the universal enveloping algebra, and at the end, give the deformed mass shells and Lorentz transformation.

GENERALIZED SKLYANIN ALGEBRA

1991 ◽  
Vol 06 (39) ◽  
pp. 3635-3640 ◽  
Author(s):  
YAS-HIRO QUANO ◽  
AKIRA FUJII
Keyword(s):  
Lie Algebra ◽  
Universal Enveloping Algebra ◽  
Baxter Equation ◽  
Enveloping Algebra ◽  
Elliptic Solutions ◽  
Sklyanin Algebra

We propose a [Formula: see text]-Sklyanin algebra to shed new light on elliptic solutions of the Yang–Baxter equation. This object gives a quadratic generalization of the universal enveloping algebra of the Lie algebra [Formula: see text]. We also clarify the meaning of the parameters contained in it.

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.

REALIZATIONS OF A REFLECTION QUADRATIC ALGEBRA RELATED TO SUq(N)

1993 ◽  
Vol 08 (36) ◽  
pp. 3467-3474
Author(s):  
C. QUESNE
Keyword(s):  
Universal Enveloping Algebra ◽  
Quadratic Algebra ◽  
R Matrix ◽  
Creation And Annihilation Operators ◽  
Enveloping Algebra

The operators bilinear in SU q(n)-covariant q-bosonic or q-fermionic creation and annihilation operators are shown to generate two different realizations of a q-deformation of the u(n) universal enveloping algebra. By adding some appropriate constants, such operators can be transformed into the generators of a reflection quadratic algebra related to the R-matrix of SU q(n). The latter generalizes to arbitrary n an algebra studied by Kulish and Sklyanin in the n=2 case. Both algebras considered here are SU q(n)-comodule.

scholarly journals DG Poisson algebra and its universal enveloping algebra

2016 ◽  
Vol 59 (5) ◽  
pp. 849-860 ◽  
Author(s):  
JiaFeng Lü ◽  
XingTing Wang ◽  
GuangBin Zhuang
Keyword(s):  
Poisson Algebra ◽  
Universal Enveloping Algebra ◽  
Enveloping Algebra
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