Related papers: Multiparametric quantum gl(2): Lie bialgebras, qua…
In this paper we introduce a multiparameter version of the quantum universal enveloping superalgebras introduced by Yamane in [H. Yamane, "Quantized enveloping algebras associated to simple Lie superalgebras and their universal…
A theory of canonical basis for a two-parameter quantum algebra is developed in parallel with the one in one-parameter case. A geometric construction of the negative part of a two-parameter quantum algebra is given by using mixed perverse…
We introduce the notion of formal multiparameter quantum universal enveloping algebras - in short FoMpQUEA - as a straightforward generalization of Drinfeld's quantum group. Then we show that the class of FoMpQUEA's is closed under…
Quantum duality principle is applied to study classical limits of quantum algebras and groups. For a certain type of Hopf algebras the explicit procedure to construct both classical limits is presented. The canonical forms of quantized…
An explicit realization of the W(2,2) Lie algebra is presented using the famous bosonic and fermionic oscillators in physics, which is then used to construct the q-deformation of this Lie algebra. Furthermore, the quantum group structures…
We introduce a two-parameter deformation of 2x2 matrices without imposing any condition on the matrices and give the universal R-matrix of the nonstandard quantum group which satisfies the quantum Yang-Baxter relation. Although in the…
We analyze among all possible quantum deformations of the 3+1 (anti)de Sitter algebras, so(3,2) and so(4,1), which have two specific non-deformed or primitive commuting operators: the time translation/energy generator and a rotation. We…
We study Galois and bi-Galois objects over the quantum group of a nondegenerate bilinear form, including the quantum group Oq(SL2). We obtain the classification of these objects up to isomorphism and some partial results for their…
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…
Quantum superalgebras $su_{q}(m\mid n)$ are studied in the framework of $R$-matrix formalism. Explicit parametrization of $L^{(+)}$ and $L^{(-)}$ matrices in terms of $su_{q}(m\mid n)$ generators are presented. We also show that quantum…
We develop the Baxterization approach to (an extension of) the quantum group GL_q(2). We introduce two matrices which play the role of spectral parameter dependent L-matrices and observe that they are naturally related to two different…
Quantum de Rham complexes on the quantum plane and the quantum group itself are constructed for the Zakrewski deformation of $ Fun ( SL(2)) $. As a by-product a new deformation of the two dimensional Heisenberg algeb ra is constructed which…
A simpler definition for a class of two-parameter quantum groups associated to semisimple Lie algebras is given in terms of Euler form. Their positive parts turn out to be 2-cocycle deformations of each other under some conditions. An…
Using the multi-parametric deformation of the algebra of functions on $ \GL{n+1} $ and the universal enveloping algebra $ \U{\igl{n+1}} $, we construct the multi-parametric quantum groups $ \IGLq{n} $ and $ \Uq{\igl{n}} $.
We refute a recent claim in the literature of a "new" quantum deformation of GL(2).
Quantum multiparameter deformation of real Clifford algebras is proposed. The corresponding irreducible representations are found.
The physical interpretation of the main notions of the quantum group theory (coproduct, representations and corepresentations, action and coaction) is discussed using the simplest examples of $q$-deformed objects (quantum group…
The notion of quantum algebras is merged with that of Lie systems in order to establish a new formalism called Poisson-Hopf algebra deformations of Lie systems. The procedure can be naturally applied to Lie systems endowed with a symplectic…
The main notions of the quantum groups: coproduct, action and coaction, representation and corepresentation are discussed using simplest examples: $GL_q(2)$, $sl_q(2)$, $q$-oscillator algebra ${\cal A}(q)$, and reflection equation algebra.…
We use the theory of the quantum group $U_q(gl(2,\RR))$ in order to develop a quantum theory of invariants and show a decomposition of invariants into a Gordan-Capelli series. Higher binary forms are introduced on the basis of braided…