Related papers: Non-standard quantum (1+1) Poincar\'e group: a $T$…
The unitary irreducible representations of a Lie group defines the Hilbert space on which the representations act. If this Lie group is a physical quantum dynamical symmetry group, this Hilbert space is identified with the physical quantum…
The most common nonlinear deformations of the su(2) Lie algebra, introduced by Polychronakos and Ro\v cek, involve a single arbitrary function of J_0 and include the quantum algebra su_q(2) as a special case. In the present contribution,…
We review the construction of the multiparametric quantum group $ISO_{q,r}(N)$ as a projection from $SO_{q,r}(N+2) $ and show that it is a bicovariant bimodule over $SO_{q,r}(N)$. The universal enveloping algebra $U_{q,r}(iso(N))$,…
We propose a definition of a Poincar\'e algebra for a two dimensional space--time with one discretized dimension. This algebra has the structure of a Hopf algebra. We use the link between Onsager's uniformization of the Ising model and the…
We show that the $\kappa$-deformed Poincar\'e quantum algebra proposed for elementary particle physics has the structure of a Hopf agebra bicrossproduct $U(so(1,3))\cobicross T$. The algebra is a semidirect product of the classical Lorentz…
We study a quantum mechanics with the usual postulates but in which the Heisenberg algebra of canonical commutation relations and the Poincare algebra are replaced by the Lie algebra of the homogeneous Lorentz group SO(5,1). It arises from…
We prove that the extended Poincare group in (1+1) dimensions is non-nilpotent solvable exponential, and therefore that it belongs to type I. We determine its first and second cohomology groups in order to work out a classification of the…
The quantum deformed (1+1) Poincare' algebra is shown to be the kinematical symmetry of the harmonic chain, whose spacing is given by the deformation parameter. Phonons with their symmetries as well as multiphonon processes are derived from…
It is noted that the single-variable Heisenberg commutation relation contains the symmetry of the $Sp(2)$ group which is isomorphic to the Lorentz group applicable to one time-like dimension and two space-like dimensions, known as the…
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…
In this paper, we present an approach to the definition of multiparameter quantum groups by studying Hopf algebras with triangular decomposition. Classifying all of these Hopf algebras which are of what we call weakly separable type over a…
We consider finite-dimensional Hopf algebras $u$ which admit a smooth deformation $U\to u$ by a Noetherian Hopf algebra $U$ of finite global dimension. Examples of such Hopf algebras include small quantum groups over the complex numbers,…
In this paper, using a Hopf-algebraic method, we construct deformed Poincar\'e SUSY algebra in terms of twisted (Hopf) algebra. By adapting this twist deformed super-Poincar\'e algrebra as our fundamental symmetry, we can see the…
The three quantum groups dual to the generalized twist deformed Poincare Hopf algebras are provided with use of FRT procedure. Their Galilean counterparts are obtained by nonrelativistic contraction scheme.
In recent papers of the author, a method was developed for constructing quasitriangular Hopf algebras (quantum groups) of the quantum-double type. As a by-product, a novel non-standard example of the quantum double has been found. In the…
For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite dimensional Lie algebra, it is known how to introduce an extension playing the role of the corresponding noncommutative phase…
A nonlinear change of basis allows to show that the non-standard quantum deformation of the (3+1) Poincare algebra has a bicrossproduct structure. Quantum universal R-matrix, Pauli-Lubanski and mass operators are presented in the new basis.
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…
The Heisenberg double of a Hopf algebra may be regarded as a quantum analogue of the cotangent bundle of a Lie group. Quantum duality principle describes relations between a Hopf algebra, its dual, and their Heisenberg double in a way which…
An elliptic two-parameter deformation of the (universal enveloping superalgebra of) affine Lie superalgebra $osp(1|2)^{(1)}$ is proposed in terms of free boson realization. This deformed superalgebra is shown to fit in the framework of…