Related papers: Non-standard quantum algebra $\mathcal{U}_h (\math…

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…

This paper together with the previous one (arXiv:hep-th/0604146) presents the detailed description of all quantum deformations of D=4 Lorentz algebra as Hopf algebra in terms of complex and real generators. We describe here in detail two…

Using the contraction procedure introduced by us in Ref. \cite{ACC2}, we construct, in the first part of the present letter, the Jordanian quantum Hopf algebra ${\cal U}_{\sf h}(sl(3))$ which has a remarkably simple coalgebraic structure…

The quantum deformation of the Jordanian twist F_qJ for the standard quantum Borel algebra U_q(B) is constructed. It gives the family U_qJ(B) of quantum algebras depending on parameters x and h. In a generic point these algebras represent…

Representation theory for the Jordanian quantum algebra U=U_h(sl(2)) is developed using a nonlinear relation between its generators and those of sl(2). Closed form expressions are given for the action of the generators of U on the basis…

Quantum $n$-qubit states that are totally symmetric under the permutation of qubits are essential ingredients of important algorithms and applications in quantum information. Consequently, there is significant interest in developing methods…

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…

Recently, a class of transformations of $R_q$-matrices was introduced such that the $q \to 1$ limit gives explicit nonstandard $R_h$-matrices. The transformation matrix is singular as $q \to 1$. For the transformed matrix, the…

Dicke states are completely symmetric states of multiple qubits (2-level systems), and qudit Dicke states are their $d$-level generalization. We define here $q$-deformed qudit Dicke states using the quantum algebra $su_q(d)$. We show that…

In this article we propose a new and so-called holomorphic deformation scheme for locally convex algebras and Hopf algebras. Essentially we regard converging power series expansion of a deformed product on a locally convex algebra, thus…

Nonstandard q-deformed algebras U'_q(so_n), proposed a decade ago for the needs of representation theory, essentially differ from the standard Drinfeld-Jimbo quantum deformation of the algebras U(so_n) and possess with regard to the latter…

Let $\hat{\mathfrak{g}}$ be an untwisted affine Kac-Moody algebra, with its Sklyanin-Drinfel'd structure of Lie bialgebra, and let $\hat{\mathfrak{h}}$ be the dual Lie bialgebra. By dualizing the quantum double construction - via formal…

Starting from the classical r-matrix of the non-standard (or Jordanian) quantum deformation of the sl(2,R) algebra, new triangular quantum deformations for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously constructed…

A systematic computational approach for the explicit construction of any quantum Hopf algebra (U_z(g),\Delta_z) starting from the Lie bialgebra (g,\delta) that gives the first-order deformation of the coproduct map \Delta_z is presented.…

A quantum algebra $U_{p,q}(\zeta ,H,X_\pm )$ associated with a nonstandard $R$-matrix with two deformation parameters$(p,q)$ is studied and, in particular, its universal ${\cal R}$-matrix is derived using Reshetikhin's method. Explicit…

Using duality and topological theory of well behaved Hopf algebras (as defined in [2]) we construct star-product models of non compact quantum groups from Drinfeld and Reshetikhin standard deformations of enveloping Hopf algebras of simple…

A two-parametric generalization of the Jordanian deformation $U_h (sl(2))$ of $sl(2)$ is presented. This involves Jacobian elliptic functions. In our deformation $U_{(h,k)}(sl(2))$, for $k^2=1$ one gets back $U_h(sl(2))$. The constuction is…

The recent focus on deformations of algebras called quantum algebras can be attributed to the fact that they appear to be the basic algebraic structures underlying an amazingly diverse set of physical situations. To date many interesting…

Any deformation of a Weyl or Clifford algebra A can be realized through a `deforming map', i.e. a formal change of generators in A. This is true in particular if A is covariant under a Lie algebra g and its deformation is induced by some…

The quantum superalgebra $U_q[gl(2/1)]$ is given as both a Drinfel'd--Jimbo deformation of $U[gl(2/1)]$ and a Hopf superalgebra. Finite--dimensional representations of this quantum superalgebra are constructed and investigated in a basis of…