R. Chakrabarti

The Gervais-Neveu-Felder equation for the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra (2007)

We note that the recently introduced fuzzy torus can be regarded as a q-deformed parafermion. Based on this picture, classification of the Hermitian representations of the fuzzy torus is carried out....

Chakrabarti, A., Chakrabarti, R.

Using a contraction procedure, we construct a twist operator that satisfies a shifted cocycle condition, and leads to the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra. The corresponding universal...

Addendum to "On Super-Jordanian ${\cal U}_{\sf h}(sl(N|1))$ Algebra (2007)

Abdesselam, B., Chakrabarti, A., Chakrabarti, R., Yanallah, A., Zahaf, M. B.

We give a complete proof of the result (2.10) presented in our paper published in J. Phys. A: Math. Gen. 39 (2006) 8307.

Basic Hypergeometric Functions and Covariant Spaces for Even Dimensional Representations of U_q[osp(1/2)] (2007)

Aizawa, N., Chakrabarti, R., Mohammed, S. S. Naina, Segar, J.

Representations of the quantum superalgebra U_q[osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the...

Universal T-matrix, Representations of OSp_q(1/2) and Little Q-Jacobi Polynomials (2006)

Aizawa, N., Chakrabarti, R., Mohammed, S. S. Naina, Segar, J.

We obtain a closed form expression of the universal T-matrix encapsulating the duality of the quantum superalgebra U_q[osp(1/2)] and the corresponding supergroup OSp_q(1/2). The classical q-->1 limit...

New connection formulae for the q-orthogonal polynomials via a series expansion of the q-exponential (2006)

Chakrabarti, R., Jagannathan, R., Mohammed, S. S. Naina

Using a realization of the q-exponential function as an infinite multiplicative sereis of the ordinary exponential functions we obtain new nonlinear connection formulae of the q-orthogonal...

On super-Jordanian ${\cal U}_{\sf h}(sl(N|1))$ algebra (2005)

Abdesselam, B., Chakrabarti, A., Chakrabarti, R., Yanallah, A., Zahaf, M. B.

A nonlinear realisation of the nonstandard (super-Jordanian) deformed ${\cal U}_{\sf h}(sl(N|1))$ algebra is given for arbitrary $N$.

Noncommutative Superspaces Covariant Under $OSp_q(1|2)$ Algebra (2005)

Quantum Spheres for OSp_q(1/2) (2005)

Using the corepresentation of the quantum group $ SL_q(2)$ a general method for constructing noncommutative spaces covariant under its coaction is developed. The method allows us to treat the quantum...

Jordanian Quantum Algebra ${\\cal U}_{\\sf h}(sl(N))$ via Contraction Method and Mapping (2005)

Using the corepresentation of the quantum supergroup OSp_q(1/2) a general method for constructing noncommutative spaces covariant under its coaction is developed. In particular, a one-parameter...

Jordanian Quantum (Super)Algebras $U_{h}(g)$ via Contraction Method and Mapping:Review (2004)

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...

Abdesselam, B., Chakrabarti, R., Yanallah, A., Zahaf, M. B.

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...

Noncommutative Geometry of Super-Jordanian $OSp_h(2/1)$ Covariant Quantum Space (2003)

On Nonstandard Quantizations of osp(2|1) Superalgebra via Contraction and Mapping (2003)

Extending a recently proposed procedure of construction of various elements of diffential geometry on noncommutative algebras, we obtain these structures on noncommutative superalgebras. As an...

Abdesselam, B., Chakrabarti, R., Hazzab, A., Yanallah, A.

We develop a generic reprersentation-independent contraction procedure for obtaining, for instance, $R_{\sf h}$ and $L$ operators of arbitrary dimensions for the quantized ${\cal U}_{\sf...

Entanglement via Barut-Girardello coherent state for $su_{q}(1, 1)$ quantum algebra: bipartite composite system (2003)

Chakrabarti, R., Vasan, S. S.

Using noncocommutative coproduct properties of the quantum algebras, we introduce and obtain, in a bipartite composite system, the Barut-Girardello coherent state for the q-deformed $su_{q}(1,1)$...

Super-Jordanian Quantum Superalgebra ${\cal U}_{h}(osp(2/1))$ (2003)

Aizawa, N., Chakrabarti, R., Segar, J.

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...

Modified braid equations, Baxterizations and noncommutative spaces for the quantum groups $GL_{q}(N), SO_{q}(N)$ and $Sp_{q}(N)$ (2002)

Chakrabarti, A., Chakrabarti, R.

Modified braid equations satisfied by generalized ${\hat R}$ matrices (for a {\em given} set of group relations obeyed by the elements of ${\sf T}$ matrices ) are constructed for q-deformed quantum...

Jordanian Quantum Algebra ${\cal U}_{\sf h}(sl(N))$ via Contraction Method and Mapping (2001)

Jordanian quantum spheres (2001)

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...

Chakrabarti, R., Segar, J.

We introduce and investigate a one parameter family of quantum spaces invariant under the left (right) coactions of the group-like element ${\cal T}_{h}^{(j=1)}$ of the Jordanian function algebra...

Jordanian Quantum Algebra ${\\cal U}_{\\sf h}(sl(N))$ via Contraction Method and Mapping (2001)

Jordanian Quantum Algebra ${\\cal U}_{\\sf h}(sl(N))$ via Contraction Method and Mapping (2001)

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...

The Gervais-Neveu-Felder equation for the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra (2000)

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...

Chakrabarti, A., Chakrabarti, R.

Using a contraction procedure, we construct a twist operator that satisfies a shifted cocycle condition, and leads to the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra. The corresponding universal...

On Jordanian U_{h,\alpha}(gl(2)) Algebra and Its T Matrices Via a Contraction Method (1998)

Chakrabarti, R., Quesne, C.

The $R_h^{j_1;j_2}$ matrices of the Jordanian U$_h$(sl(2)) algebra at arbitrary dimensions may be obtained from the corresponding $R_q^{j_1;j_2}$ matrices of the standard $q$-deformed U$_q$(sl(2))...

Maps and twists relating $U(sl(2))$ and the nonstandard $U_{h}(sl(2))$: unified construction (1998)

Abdesselam, B., Chakrabarti, A., Chakrabarti, R., Segar, J.

A general construction is given for a class of invertible maps between the classical $U(sl(2))$ and the Jordanian $U_{h}(sl(2))$ algebras. Different maps are directly useful in different contexts....

On a Nonstandard Two-Parametric Quantum Algebra and Its Connections With (1998)

R. Chakrabarti, R. Jagannathan

. A quantum algebra U p;q (i; H;X Sigma ) associated with a nonstandard R-matrix with two deformation parameters(p; q) is studied and, in particular, its universal R-matrix is derived using...

On the Hopf structure of ... and the universal T-matrix of ... (1998)

R. Chakrabarti, R. Jagannathan

Using the technique developed by Fronsdal and Galindo (Lett. Math. Phys. 27 (1993) 57) for studying the Hopf duality between the quantum algebras Fun p;q (GL(2)) and U p;q (gl(2)), the Hopf structure...

General Construction of Nonstandard $R_h$-matrices as Contraction Limits of $R_{q}$-matrices (1997)

Combined (q,h)-Deformation as a Nonlinear Map on $U_q(sl(2))$ (1996)

A class of transformations of $R_q$-matrices is introduced such that the $q\to 1$ limit gives explicit nonstandard $R_{h}$-matrices. The transformation matrix is singular itself at $q\to 1$ limit....

On ${\cal U}_h(sl(2))$, ${\cal U}_h(e(3))$ and their Representations (1996)

The generators $(J_{\pm}, J_0)$ of the algebra $U_q(sl(2))$ is our starting point. An invertible nonlinear map involving, apart from q, a second arbitrary complex parameter h, defines a triplet...

Irreducible Representations of Jordanian Quantum Algebra ${\cal U}_h(sl(2))$ Via a Nonlinear Map (1996)

By solving a set of recursion relations for the matrix elements of the ${\cal U}_h(sl(2))$ generators, the finite dimensional highest weight representations of the algebra were obtained as factor...

The dual $(p,q)$-Alexander-Conway Hopf algebras and the associated universal ${\cal T}$-matrix (1996)

The generators of the Jordanian quantum algebra ${\cal U}_h(sl(2))$ are expressed as nonlinear invertible functions of the classical $sl(2)$ generators. This permits immediate explicit construction...

Finite-dimensional Calogero representation of the $q$-differential operator (1995)

The dually conjugate Hopf algebras $Fun_{p,q}(R)$ and $U_{p,q}(R)$ associated with the two-parametric $(p,q)$-Alexander-Conway solution $(R)$ of the Yang-Baxter equation are studied. Using the Hopf...

On a nonstandard two-parametric quantum algebra and its connections with $U_{p,q}(gl(2))$ and $U_{p,q}(gl(1|1))$ (1994)

A finite-dimensional matrix representation of the Jackson $q$-differential operator $D_q$, defined by $D_qf(x)$ $=$ $(f(qx)-f(x))/(x(q-1))$, is written down following Calogero. Such a representation...

On the Hopf structure of $U_{p,q}(gl(1|1))$ and the universal ${\cal T}$-matrix of $Fun_{p,q}(GL(1|1))$ (1994)

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...