Fractional Super Lie Algebras and Groups

n^{th} root of a Lie algebra and its dual (that is fractional supergroup) based on the permutation group $S_n$ invariant forms are formulated in the Hopf algebra formalism. Detailed discussion of $S_3$-graided $sl(2)$ algebras is done.Comment: 13 pages, detailed discussion of $S_3$-graided $sl(2)$ is adde

Braided Oscillators

The braided Hopf algebra structure of the generalized oscillator is investigated. Using the solutions two types of braided Fibonacci oscillators are introduced. This leads to two types of braided Biedenharn-Macfarlane oscillators.Comment: 12 pages, latex, some references added, published versio

Casimir Energy for a Wedge with Three Surfaces and for a Pyramidal Cavity

Casimir energy calculations for the conformally coupled massless scalar field for a wedge defined by three intersecting planes and for a pyramid with four triangular surfaces are presented. The group generated by reflections are employed in the formulation of the required Green functions and the wave functions.Comment: Latex, 9 page

Electromagnetic Fields of Slowly Rotating Magnetized Gravastars

We study the dipolar magnetic field configuration and present solutions of Maxwell equations in the internal background spacetime of a a slowly rotating gravastar. The shell of gravastar where magnetic field penetrated is modeled as sphere consisting of perfect highly magnetized fluid with infinite conductivity. Dipolar magnetic field of the gravastar is produced by a circular current loop symmetrically placed at radius $a$ at the equatorial plane.Comment: 5 pages, 2 figures, accepted for publication to Mod. Phys. Lett.

Scalar Casimir effect between two concentric D-dimensional spheres

The Casimir energy for a massless scalar field between the closely spaced two concentric D-dimensional (for D>3) spheres is calculated by using the mode summation with contour integration in the complex plane of eigenfrequencies and the generalized Abel-Plana formula for evenly spaced eigenfrequency at large argument. The sign of the Casimir energy between closely spaced two concentric D-dimensional spheres for a massless scalar field satisfying the Dirichlet boundary conditions is strictly negative. The Casimir energy between D-1 dimensional surfaces close to each other is regarded as interesting both by itself and as the key to describing of stability of the attractive Casimir force. PACS number(s): 03.70.+k, 11.10.Kk, 11.10.Gh, 03.65.GeComment: 14 pages. arXiv admin note: substantial text overlap with arXiv:1207.418

On Properties of Vacuum Axial Symmetric Spacetime of Gravitomagnetic Monopole in Cylindrical Coordinates

We investigate general relativistic effects associated with the gravitomagnetic monopole moment of gravitational source through the analysis of the motion of test particles and electromagnetic fields distribution in the spacetime around nonrotating cylindrical NUT source. We consider the circular motion of test particles in NUT spacetime, their characteristics and the dependence of effective potential on the radial coordinate for the different values of NUT parameter and orbital momentum of test particles. It is shown that the bounds of stability for circular orbits are displaced toward the event horizon with the growth of monopole moment of the NUT object. In addition, we obtain exact analytical solutions of Maxwell equations for magnetized and charged cylindrical NUT stars.Comment: 16 pages, 3 figures, 1 tabl

External Electromagnetic Fields of a Slowly Rotating Magnetized Star with Gravitomagnetic Charge

We study Maxwell equations in the external background spacetime of a slowly rotating magnetized NUT star and find analytical solutions for the exterior electric fields after separating the equations of electric field into angular and radial parts in the lowest order approximation. The star is considered isolated and in vacuum, with dipolar magnetic field aligned with the axis of rotation. The contribution to the external electric field of star from the NUT charge is considered in detail.Comment: 6 pages, 2 figures, accepted for publication in Astrophysics and Space Scienc