Related papers: The quantum 2-dimensional Poincare group from quan…
We construct the induced representations of the null-plane quantum Poincar\'e and quantum kappa Galilei algebras in (1+1) dimensions. The induction procedure makes use of the concept of module and is based on the existence of a pair of Hopf…
We describe the quantum $\kappa$-deformation of super-Poincar\'{e} algebra, with fundamental mass-like deformation parameter $\kappa$. We shall describe the result in graded bicrossproduct basis, with classical Lorentz superalgebra sector…
Quantum algebras (also called quantum groups) are deformed versions of the usual Lie algebras, to which they reduce when the deformation parameter q is set equal to unity. From the mathematical point of view they are Hopf algebras. Their…
We construct two-parameter deformation of an universal enveloping algebra $U(g[u])$ of a polynomial loop algebra $g[u]$, where $g$ is a finite-dimensional complex simple Lie algebra (or superalgebra). This new quantum Hopf algebra called…
We discuss a general construction of a deformation of a smash product algebra coming from an action of a particular Hopf algebra. This Hopf algebra is generated by skew-primitive and group-like elements, and depends on a complex parameter.…
In this paper, we mainly focus on a new type quantum group $U_{q}(\mathfrak{sl}^{*}_2)$ and its Hopf PBW-deformations $U_{q}(\mathfrak{sl}^{*}_2,\kappa)$ in which $U_{q}(\mathfrak{sl}^{*}_2,0) = U_{q}(\mathfrak{sl}^{*}_2)$ and the classical…
This paper discusses the notion of a deformation quantization for an arbitrary polynomial Poisson algebra A. We examine the Hochschild cohomology group H^3(A) and find that if a deformation of A exists it can be given by bidifferential…
It is known that the inhomogeneous quantum group IGL_{q,r}(2) can be constructed as a quotient of the multiparameter q-deformation of GL(3). We show that a similar result holds for the inhomogeneous Jordanian deformation and exhibit its…
We propose a nonstandard approach to solving the apparent incompatibility between the coalgebra structure of some inhomogeneous quantum groups and their natural complex conjugation. In this work we sketch the general idea and develop the…
The general framework of bicrossproduct Hopf algebras given by Majid is extended to $Z_2$-graded bicrossproduct Hopf superalgebras. As examples of bicrossproduct Hopf superalgebras we provide the graded algebras of functions on undeformed…
Quantum deformations of (anti-)de Sitter algebras in (2+1) dimensions are revisited, and several features of these quantum structures are reviewed. In particular, the classification problem of (2+1) (A)dS Lie bialgebras is presented and the…
The Lie algebra of the classical group SU(2) is constructed from two quon algebras for which the deformation parameter is a common root of unity. This construction leads to (i) a not very well-known polar decomposition of the ladder…
Nonlinear deformations of the enveloping algebra of su(2), involving two arbitrary functions of J_0 and generalizing the Witten algebra, were introduced some time ago by Delbecq and Quesne. In the present paper, the problem of endowing some…
Intrinsic Hopf algebra structure of the Woronowicz differential complex is shown to generate quite naturally a bicovariant algebra of four basic objects within a differential calculus on quantum groups -- coordinate functions, differential…
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…
2-Dim quantum Poincare` Group E_q(1,1) at roots of unity, its dual U_q(e(1,1)) and some of its homogeneous spaces are introduced. Invariant integrals on E_q(1,1) and its invariant discrete subgroup E(1,1\mid p) are constructed.…
A new deformation of the of the Poincar\'e group and of the Minkowski space-time is given. From the mathematical point of view this deformation is rather quantum-braided group. Global and local structure of this quantum-braided Poincar\'e…
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
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…
The $\kappa$-deformation of the (2+1)D anti-de Sitter, Poincar\'e and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter.…