Related papers: Super-Jordanian Quantum Superalgebra ${\cal U}_{h}…
The algebra H of the dual -1 Hahn polynomials is derived and shown to arise in the Clebsch-Gordan problem of sl_{-1}(2). The dual -1 Hahn polynomials are the bispectral polynomials of a discrete argument obtained from a q-> -1 limit of the…
We study the topologically twisted osp(2|2)+osp(2|2) conformal superalgebra. The algebra includes the Lagrangians which are intrinsic to the topological field theory and composed of fermionic generators. Studying the Lagrangians through a…
It is shown that the deformed Heisenberg algebra involving the reflection operator R (R-deformed Heisenberg algebra) has finite-dimensional representations which are equivalent to representations of paragrassmann algebra with a special…
We show that certain twisting deformations of a family of supersolvable groups are simple as Hopf algebras. These groups are direct products of two generalized dihedral groups. Examples of this construction arise in dimensions 60 and…
We describe in detail two-parameter nonstandard quantum deformation of D=4 Lorentz algebra $\mathfrak{o}(3,1)$, linked with Jordanian deformation of $\mathfrak{sl} (2;\mathbb{C})$. Using twist quantization technique we obtain the explicit…
A supersymmetric extension of the Hahn algebra is introduced. This quadratic superalgebra, which we call the Hahn superalgebra, is constructed using the realization provided by the Dunkl oscillator model in the plane, whose Hamiltonian…
A unitary orthosymplectic quantum supergroup is introduced. Two covariant differential calculi on the quantum superspace $SP_q^{1|2}$ are presented. The $h$-deformed symplectic superspaces via a contraction of the $q$-deformed symplectic…
The centrally extended superalgebra psu(2|2)xR^3 was shown to play an important role for the integrable structures of the one-dimensional Hubbard model and of the planar AdS/CFT correspondence. Here we consider its quantum deformation…
We realize the Hopf algebra $U_{q^{-1}}(so(N))$ as an algebra of differential operators on the quantum Euclidean space ${\bf R}_q^N$. The generators are suitable q-deformed analogs of the angular momentum components on ordinary ${\bf R}^N$.…
The Jordanian deformation of $sl(2)$ bi-algebra structure is studied in view of physical applications to breaking of conformal symmetry in the high energy asymptotics of scattering. Representations are formulated in terms of polynomials,…
A description of the orthosymplectic Lie superalgebra $osp(2n+1/2m)$ and also of its $q-$deformed analogue $U_q[osp(2n+1/2m)]$ in terms of a new set of generators, called Green generators, is given. These generators are very different form…
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 argue that the algebra $W_q(n)$, generated by $n$ pairs of deformed $q$-bosons, does not allow a Hopfalgebra structure. To this end we show that it is impossible to define a comultiplication even for the usual, nondeformed case. We…
Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebra and root vectors and which make it possible to construct representations by operators acting…
Abstr.: The classical r-matrix implied by the quantum k-Poincare algebra of Lukierski,Nowicki and Ruegg is used to generate a Poisson structure on the ISL(2,C) group. A quantum deformation of the ISL(2,C) group ( on the Hopf algebra level )…
A large family of "standard" coboundary Hopf algebras is investigated. The existence of a universal R-matrix is demonstrated for the case when the parameters are in general position. Special values of the parameters are characterized by the…
We discuss quantum deformation of the affine transformation algebra. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators.
Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are…
The two-parametric quantum superalgebra $U_{pq}[gl(2/2)]$ and its representations are considered. All finite-dimensional irreducible representations of this quantum superalgebra can be constructed and classified into typical and nontypical…
A Lagrangian of the topological field theory is found in the twisted osp(2|2)\oplus osp(2|2)conformal super algebra. The reduction on a moduli space is then elaborated through the vanishing Noether current.