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 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 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.

On the semicenter of a universal enveloping algebra of a lie superalgebra

1994 ◽  
Vol 22 (15) ◽  
pp. 6471-6492
Author(s):  
K. Bauwens ◽  
A.I. Ooms ◽  
P. Wauters
Keyword(s):  
Lie Superalgebra ◽  
Universal Enveloping Algebra ◽  
Enveloping Algebra

Deformation of the Universal Enveloping Algebra of Γ (σ1, σ2, σ3)

1996 ◽  
Vol 39 (4) ◽  
pp. 499-506 ◽  
Author(s):  
Yi Ming Zou
Keyword(s):  
Lie Superalgebra ◽  
Universal Enveloping Algebra ◽  
Enveloping Algebra ◽  
Defining Relations ◽  
Basis Theorem

AbstractThe defining relations for the Lie superalgebra Γ (σ1, σ2, σ3) as a contragredient algebra are discussed and a PBW type basis theorem is proved for the corresponding q-deformation.

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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