165 research outputs found
Customized television: Standards compliant advanced digital television
This correspondence describes a European Union supported collaborative project called CustomTV based on the premise that future TV sets will provide all sorts of multimedia information and interactivity, as well as manage all such services according to each userâs or group of userâs preferences/profiles. We have demonstrated the potential of recent standards (MPEG-4 and MPEG-7) to implement such a scenario by building
the following services: an advanced EPG, Weather Forecasting, and Stock Exchange/Flight Information
New time-type and space-type non-standard quantum algebras and discrete symmetries
Starting from the classical r-matrix of the non-standard (or Jordanian)
quantum deformation of the sl(2,R) algebra, new triangular quantum deformations
for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously
constructed by using a graded contraction scheme; these are realized as
deformations of conformal algebras of (1+1)-dimensional spacetimes. Time-type
and space-type quantum algebras are considered according to the generator that
remains primitive after deformation: either the time or the space translation,
respectively. Furthermore by introducing differential-difference conformal
realizations, these families of quantum algebras are shown to be the symmetry
algebras of either a time or a space discretization of (1+1)-dimensional (wave
and Laplace) equations on uniform lattices; the relationship with the known Lie
symmetry approach to these discrete equations is established by means of twist
maps.Comment: 17 pages, LaTe
Jordanian Quantum Algebra via Contraction Method and Mapping
Using the contraction procedure introduced by us in Ref. \cite{ACC2}, we
construct, in the first part of the present letter, the Jordanian quantum Hopf
algebra which has a remarkably simple coalgebraic
structure and contains the Jordanian Hopf algebra ,
obtained by Ohn, as a subalgebra. A nonlinear map between and the classical algebra is then established. In the second
part, we give the higher dimensional Jordanian algebras for all . The Universal -matrix of is also given.Comment: 17 pages, Late
Bicovariant Differential Geometry of the Quantum Group
There are only two quantum group structures on the space of two by two
unimodular matrices, these are the and the [9-13] quantum
groups. One can not construct a differential geometry on , which at
the same time is bicovariant, has three generators, and satisfies the Liebnitz
rule. We show that such a differential geometry exists for the quantum group
and derive all of its properties
Jordanian Twist Quantization of D=4 Lorentz and Poincare Algebras and D=3 Contraction Limit
We describe in detail two-parameter nonstandard quantum deformation of D=4
Lorentz algebra , linked with Jordanian deformation of
. Using twist quantization technique we obtain
the explicit formulae for the deformed coproducts and antipodes. Further
extending the considered deformation to the D=4 Poincar\'{e} algebra we obtain
a new Hopf-algebraic deformation of four-dimensional relativistic symmetries
with dimensionless deformation parameter. Finally, we interpret
as the D=3 de-Sitter algebra and calculate the contraction
limit ( -- de-Sitter radius) providing explicit Hopf algebra
structure for the quantum deformation of the D=3 Poincar\'{e} algebra (with
masslike deformation parameters), which is the two-parameter light-cone
-deformation of the D=3 Poincar\'{e} symmetry.Comment: 13 pages, no figure
Degenerate Sklyanin Algebras
New trigonometric and rational solutions of the quantum Yang-Baxter equation
(QYBE) are obtained by applying some singular gauge transformations to the
known Belavin-Drinfeld elliptic R-matrix for . These
solutions are shown to be related to the standard ones by the quasi-Hopf twist.
We demonstrate that the quantum algebras arising from these new R-matrices can
be obtained as special limits of the Sklyanin algebra. A representation for
these algebras by the difference operators is found. The
-case is discussed.Comment: 12 page
Twist maps for non-standard quantum algebras and discrete Schrodinger symmetries
The minimal twist map introduced by B. Abdesselam, A. Chakrabarti, R.
Chakrabarti and J. Segar (Mod. Phys. Lett. A 14 (1999) 765) for the
non-standard (Jordanian) quantum sl(2,R) algebra is used to construct the twist
maps for two different non-standard quantum deformations of the (1+1)
Schrodinger algebra. Such deformations are, respectively, the symmetry algebras
of a space and a time uniform lattice discretization of the (1+1) free
Schrodinger equation. It is shown that the corresponding twist maps connect the
usual Lie symmetry approach to these discrete equations with non-standard
quantum deformations. This relationship leads to a clear interpretation of the
deformation parameter as the step of the uniform (space or time) lattice.Comment: 16 pages, LaTe
Multiparametric quantum gl(2): Lie bialgebras, quantum R-matrices and non-relativistic limits
Multiparametric quantum deformations of are studied through a
complete classification of Lie bialgebra structures. From them, the
non-relativistic limit leading to harmonic oscillator Lie bialgebras is
implemented by means of a contraction procedure. New quantum deformations of
together with their associated quantum -matrices are obtained and
other known quantizations are recovered and classified. Several connections
with integrable models are outlined.Comment: 21 pages, LaTeX. To appear in J. Phys. A. New contents adde
Boson representations, non-standard quantum algebras and contractions
A Gelfan'd--Dyson mapping is used to generate a one-boson realization for the
non-standard quantum deformation of which directly provides its
infinite and finite dimensional irreducible representations. Tensor product
decompositions are worked out for some examples. Relations between contraction
methods and boson realizations are also explored in several contexts. So, a
class of two-boson representations for the non-standard deformation of
is introduced and contracted to the non-standard quantum (1+1)
Poincar\'e representations. Likewise, a quantum extended Hopf
algebra is constructed and the Jordanian -oscillator algebra representations
are obtained from it by means of another contraction procedure.Comment: 21 pages, LaTeX; two new references adde
Classical integrability of Schrodinger sigma models and q-deformed Poincare symmetry
We discuss classical integrable structure of two-dimensional sigma models
which have three-dimensional Schrodinger spacetimes as target spaces. The
Schrodinger spacetimes are regarded as null-like deformations of AdS_3. The
original AdS_3 isometry SL(2,R)_L x SL(2,R)_R is broken to SL(2,R)_L x U(1)_R
due to the deformation. According to this symmetry, there are two descriptions
to describe the classical dynamics of the system, 1) the SL(2,R)_L description
and 2) the enhanced U(1)_R description. In the former 1), we show that the
Yangian symmetry is realized by improving the SL(2,R)_L Noether current. Then a
Lax pair is constructed with the improved current and the classical
integrability is shown by deriving the r/s-matrix algebra. In the latter 2), we
find a non-local current by using a scaling limit of warped AdS_3 and that it
enhances U(1)_R to a q-deformed Poincare algebra. Then another Lax pair is
presented and the corresponding r/s-matrices are also computed. The two
descriptions are equivalent via a non-local map.Comment: 20 pages, no figure, further clarification and references adde
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