986 research outputs found
The quantum Casimir operators of \Uq and their eigenvalues
We show that the quantum Casimir operators of the quantum linear group
constructed in early work of Bracken, Gould and Zhang together with one extra
central element generate the entire center of \Uq. As a by product of the
proof, we obtain intriguing new formulae for eigenvalues of these quantum
Casimir operators, which are expressed in terms of the characters of a class of
finite dimensional irreducible representations of the classical general linear
algebra.Comment: 10 page
A symmetry invariant integral on kappa-deformed spacetime
In this note we present an approach using both constructive and Hopf
algebraic methods to contribute to the not yet fully satisfactory definition of
an integral on kappa-deformed spacetime. The integral presented here is based
on the inner product of differential forms and it is shown that this integral
is explicitly invariant under the deformed symmetry structure.Comment: 16 page
On two theorems for flat, affine group schemes over a discrete valuation ring
We include short and elementary proofs of two theorems characterizing
reductive group schemes over a discrete valuation ring, in a slightly more
general context.Comment: 10 pages. To appear in C. E. J.
Chaotic Accretion in a Non-Stationary Electromagnetic Field of a Slowly Rotating Compact Star
We investigate charge accretion in vicinity of a slowly rotating compact star
with a non-stationary electromagnetic field. Exact solutions to the general
relativistic Maxwell equations are obtained for a star formed of a highly
degenerate plasma with a gravitational field given by the linearized Kerr
metric. These solutions are used to formulate and then to study numerically the
equations of motion for a charged particle in star's vicinity using the
gravitoelectromagnetic force law. The analysis shows that close to the star
charge accretion does not always remain ordered. It is found that the magnetic
field plays the dominant role in the onset of chaos near the star's surface.Comment: 9 pages, 4 figure
Investigating Iowa\u27s Weeds
The term weed is often defined as a plant out of place. A. C. Martin has complained that this definition reflects human bias and that pest plants are out of place only with respect to man\u27s immediate purpose. In nature\u27s scheme, they often serve useful functions such as providing food for wildlife throughout the growing season and covering barren soil, thus preventing soil erosion. Judging from their competitive success with many so-called desirable species, they are anything but out of place
Notes on two-parameter quantum groups, (I)
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 operator realization of the positive part is given.Comment: 11 page
Restricted infinitesimal deformations of restricted simple Lie algebras
We compute the restricted infinitesimal deformations of the restricted simple
Lie algebras over an algebraically closed field of characteristic different
from 2 and 3.Comment: 15 pages; final version, to appear in Journal of Algebra and Its
Application
Scaling Solutions and reconstruction of Scalar Field Potentials
Starting from the hypothesis of scaling solutions, the general exact form of
the scalar field potential is found. In the case of two fluids, it turns out to
be a negative power of hyperbolic sine. In the case of three fluids the
analytic form is not found, but is obtained by quadratures.Comment: 5 pages, 2 figures, some changes in references and figures caption
Circular holonomy in the Taub-NUT spacetime
Parallel transport around closed circular orbits in the equatorial plane of
the Taub-NUT spacetime is analyzed to reveal the effect of the gravitomagnetic
monopole parameter on circular holonomy transformations. Investigating the
boost/rotation decomposition of the connection 1-form matrix evaluated along
these orbits, one finds a situation that reflects the behavior of the general
orthogonally transitive stationary axisymmetric case and indeed along Killing
trajectories in general.Comment: 9 pages, LaTeX iopart class, no figure
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