Related papers: Oscillator Quantum Algebra and Deformed su(2) Alge…
We consider a problem which may be viewed as an inverse one to the Schwinger realization of Lie algebra, and suggest a procedure of deforming the so-obtained algebra. We illustrate the method through a few simple examples extending…
The shift operator for a quantum lattice current algebra associated with sl(2) is produced in the form of product of local factors. This gives a natural deformation of the Sugawara construction for discrete space-time.
A superintegrable finite model of the quantum isotropic oscillator in two dimensions is introduced. It is defined on a uniform lattice of triangular shape. The constants of the motion for the model form an SU(2) symmetry algebra. It is…
A noncommutative algebra of the complex $q$-twistors and their differentials is considered on the basis of the quantum $GL_q (4)\times SL_q (2)$ group. Real and pseudoreal $q$-twistors are discussed too. We consider the quantum-group…
We discuss the left-covariant 3-dimensional differential calculus on the quantum sphere $SU_q (2)/U(1) $. The $SU_q (2)$-spinor harmonics are treated as coordinates of the quantum sphere. We consider the gauge theory for the quantum group…
The symmetry algebra of the two-dimensional quantum harmonic oscillator with rational ratio of frequencies is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are…
We show that our construction of realizations for Lie algebras and quantum algebras can be generalized to quantum superalgebras, too. We study an example of quantum superalgebra $U_q(gl(2/1))$ and give the boson-fermion realization with…
Starting from a faithful five-dimensional matrix representation of the group of two independent oscillators and applying the R-matrix method we generate some classes of deformed fermionic-bosonic quantum Hopf algebras. The corresponding Lie…
The unified $ (p,q; \alpha,\gamma, l)$-deformation of a number of well-known deformed oscillator algebras is introduced.The deformation is constructed by imputing new free parameters into the structure functions and by generalizing the…
All classical Lie algebras can be realized \`a la Schwinger in terms of fermionic oscillators. We show that the same can be done for their $q$-deformed counterparts by simply replacing the fermionic oscillators with anyonic ones defined on…
Four apparently different bosonizations of the $U_q(su(2)_k)$ quantum current algebra for arbitrary level $k$ have recently been proposed in the literature. However, the relations among them have so far remained unclear except in one case.…
Quantum Hall effect wavefunctions corresponding to the filling factors 1/2p+1, 2/2p+1,..., 2p/2p+1, 1, are shown to form a basis of irreducible cyclic representation of the quantum algebra U_q(sl(2)) at q^{2p+1}=1. Thus, the wavefunctions…
We study quantum deformed $gl(n)$ and $igl(n)$ algebras on a quantum space discussing multi-parametric extension. We realize elements of deformed $gl(n)$ and $igl(n)$ algebras by a quantum fermionic space. We investigate a map between…
In this paper we study the deformed statistics and oscillator algebras of quantum fields defined in $\kappa$-Minkowski spacetime. The twisted flip operator obtained from the twist associated with the star product requires an enlargement of…
It is shown that the deformed Heisenberg algebra involving the reflection operator R (R-deformed Heisenberg algebra) has finite-dimensional representations which are equivalent to representations of paragrassmann algebra with a special…
Relation between Bopp-Kubo formulation and Weyl-Wigner-Moyal symbol calculus, and non-commutative geometry interpretation of the phase space representation of quantum mechanics are studied. Harmonic oscillator in phase space via creation…
After showing that the magnetic translation operators are not the symmetries of the QHE on non-flat surfaces , we show that there exist another set of operators which leads to the quantum group symmetries for some of these surfaces . As a…
The superintegrability, wavefunctions and overlap coefficients of the Dunkl oscillator model in the plane were considered in the first part. Here finite-dimensional representations of the symmetry algebra of the system, called the…
The non-standard quantum deformation of the (trivially) extended sl(2,R) algebra is used to construct a new quantum deformation of the two-photon algebra h_6 and its associated quantum universal R-matrix. A deformed one-boson representation…
We present the most general polynomial Lie algebra generated by a second order integral of motion and one of order M, construct the Casimir operator, and show how the Jacobi identity provides the existence of a realization in terms of…