Related papers: A Generalization of $U_h(sl(2))$ via Jacobian Elli…
We introduce a universal R matrix for the Jordanian deformation of $\U{ \sl(2)}$. Using $\Uh{\so(4)}=\Uh{\sl(2)} \oplus {\rm U}_{-h}(\sl(2))$, we obtain the universal R matrix for $\Uh{\so(4)}$. Applying the graded contractions on the…
Nonrelativistic quantum mechanics and conformal quantum mechanics are deformed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian…
Using a complex deformation q=exp(is) of su(2) we obtain extensions of the finite-dimensional representations towards the infinite-dimensional ones. A generalised q-deformation of su(2), as a Hopf algebra is introduced. We present the…
Two dimensional classical integrable systems and different integrable deformations for them are derived from phase space realizations of classical $sl(2)$ Poisson coalgebras and their $q-$deformed analogues. Generalizations of Morse,…
In this article we introduce a class of generalisations of the Jordan-Schwinger (JS) map which realises the recent proposed generalised sl(2) (G-sl(2)) algebra via two independent Generalised Heisenberg Algebras (GHA). Although the GHA and…
Using crystal basis, in the space of symmetric irreducible representations, we explicitly write invertible deforming functionals between the q-deformed universal enveloping algebra and the Lie algebras sl(n) and sp(2n).For sl(2) we obtain…
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…
Hinted by the elliptic parameterization of the Ising model, the addition formula of the elliptic function forms to give the integrable SU(2) group relation in the previous paper. We then expect that the addition formula of the Abelian…
A generalization of Jacobi's elliptic functions is introduced as inversions of hyperelliptic integrals. We discuss the special properties of these functions, present addition theorems and give a list of indefinite integrals. As a physical…
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…
The $h$-deformation of functions on the Grassmann matrix group $Gr(2)$ is presented via a contraction of $Gr_q(2)$. As an interesting point, we have seen that, in the case of the $h$-deformation, both R-matrices of $GL_h(2)$ and $Gr_h(2)$…
Some one- and two-parametric deformations of U[sl(2)] and their representations are considered. Interestingly, a newly introduced two-parametric deformation admits a class of infinite - dimensional representations which have no classical…
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…
Jacobi's elliptic functions have been constructed from a deformed Lie algebra. The generators of the algebra have been obtained from a bi-orthogonal system. The deformation parameter resembles the modulus of the relevant elliptic functions.
A Hopf algebra with four generators among which an involution (reflection) operator, is introduced. The defining relations involve commutators and anticommutators. The discrete series representations are developed. Designated by…
For all three--dimensional Lie algebras the construction of generators in terms of functions on 4-dimensional real phase space is given with a realization of the Lie product in terms of Poisson brackets. This is the classical…
Representation theory for the Jordanian quantum algebra $U=U_h(sl(2))$ is developed. Closed form expressions are given for the action of the generators of U on the basis vectors of finite dimensional irreducible representations. It is shown…
Let $k$ be a subfield of $\mathbb{C}$ which contains all $2$-power roots of unity, and let $K = k(\alpha_{1}, \alpha_{2}, ... , \alpha_{2g + 1})$, where the $\alpha_{i}$'s are independent and transcendental over $k$, and $g$ is a positive…
The contraction and Jordan-Schwinger construction connect the $su(2)$ and the heisenberg algebra, going in oposite directions. This persists in the q-deformed cases, but in a slightly different way. This work investigates this further,…
A two-parametric deformation of U[sl(2)] and its representations are considered. This newly introduced two-parametric quantum group denoted as $U_{pq}[sl(2)]$ admits a class of infinite-dimensional representations which have no classical…