相关论文: Nonstandard Poincare and Heisenberg Algebras
The Hopf algebra dual form for the non--standard uniparametric deformation of the (1+1) Poincar\'e algebra $iso(1,1)$ is deduced. In this framework, the quantum coordinates that generate $Fun_w(ISO(1,1))$ define an infinite dimensional Lie…
A new derivation of the quantum deformation of the 2 dimensional Euclidean Poincare group (cf S. Zakrzewski) is proposed. It is based on a contraction of the Hopf algebra Fun(SO_q(3)). The deformation parameter q is sent to one, as in the…
A new "non-standard" quantization of the universal enveloping algebra of the split (natural) real form $so(2,2)$ of $D_2$ is presented. Some (classical) graded contractions of $so(2,2)$ associated to a $Z_2 \times Z_2$ grading are studied,…
Contracting the $h$-deformation of $\SL(2,\Real)$, we construct a new deformation of two dimensional Poincar\'e algebra, the algebra of functions on its group and its differential structure. It is also shown that the Hopf algebra is…
A non-standard quantum deformation of the two-photon algebra $h_6$ is constructed, and its quantum universal R-matrix is given. Representations of this new quantum algebra are studied on the Fock space and translated into Fock-Bargmann…
By starting from the non-standard quantum deformation of the sl(2,R) algebra, a new quantum deformation for the real Lie algebra so(2,2) is constructed by imposing the former to be a Hopf subalgebra of the latter. The quantum so(2,2)…
A universal quasitriangular $R$--matrix for the non-standard quantum (1+1) Poincar\'e algebra $U_ziso(1,1)$ is deduced by imposing analyticity in the deformation parameter $z$. A family $g_\mu$ of ``quantum graded contractions" of the…
In this paper, we introduce non-standard deformations of (1+2)- and (2+1)-superspaces via a contraction using standard deformations of them. This deformed superspaces denoted by ${\mathbb A}_h^{1|2}$ and ${\mathbb A}_{h'}^{2|1}$,…
A new quantum deformation, which we call null-plane, of the (3+1) Poincar\'e algebra is obtained. The algebraic properties of the classical null-plane description are generalized to this quantum deformation. In particular, the classical…
The recently proposed jordanian quantization of the Lie superalgebra $osp(1|2)$ due to the embedding $sl(2) \subset osp(1|2)$, is extended including odd generators into the twisting element $\cal F$. This deformation is obtained as a…
The non-standard (Jordanian) quantum deformations of $so(2,2)$ and (2+1) Poincar\'e algebras are constructed by starting from a quantum $sl(2,\R)$ basis such that simple factorized expressions for their corresponding universal $R$-matrices…
A universal R--matrix for the quantum Heisenberg algebra h(1)q is presented. Despite of the non--quasitriangularity of this Hopf algebra, the quantum group induced from it coincides with the quasitriangular deformation already known.
A full (triangular) quantum deformation of so(3,2) is presented by considering this algebra as the conformal algebra of the 2+1 dimensional Minkowskian spacetime. Non-relativistic contractions are analysed and used to obtain quantum Hopf…
A nonlinear realisation of the nonstandard (super-Jordanian) deformed ${\cal U}_{\sf h}(sl(N|1))$ algebra is given for arbitrary $N$.
The most common nonlinear deformations of the su(2) Lie algebra, introduced by Polychronakos and Ro\v cek, involve a single arbitrary function of J_0 and include the quantum algebra su_q(2) as a special case. In the present contribution,…
The kappa-deformed dual pair of Poincare algebra and Poincare group is formulated in the framework of Heisenberg doubles. The covariant kappa-deformed phase space is described in detail as a subalgebra.The realizations of proposed algebraic…
A triangular quantum deformation of $ osp(2/1) $ from the classical $r$-matrix including an odd generator is presented with its full Hopf algebra structure. The deformation maps, twisting element and tensor operators are considered for the…
A two parametric deformation of the enveloping Heisenberg algebra ${\cal H}(4)$ which appear as a combination of the standard and a nonstandard quantization given by Ballesteros and Herranz is defined and proved to be Ribbon Hopf algebra.…
We describe Jordanian ``nonstandard'' deformation of U(osp(1|2)) by employing the twist quantization technique. An extension of these results to U(osp(1|4))describing deformed graded D=4 $AdS$ symmetries and to their super-Poincar\'{e}…
The $\hat\kappa$-deformed extended Galilei Hopf group algebra, ${\rm Fun}_{\hat\kappa}(\tilde G_{(m)})$, is introduced. It provides an example of a cocycle bicrossproduct structure, and is shown to be the contraction limit of a…