196 research outputs found
Deforming Maps for Lie Group Covariant Creation and Annihilation Operators
Any deformation of a Weyl or Clifford algebra A can be realized through a
`deforming map', i.e. a formal change of generators in A. This is true in
particular if A is covariant under a Lie algebra g and its deformation is
induced by some triangular deformation of the Hopf algebra . We
propose a systematic method to construct all the corresponding deforming maps,
together with the corresponding realizations of the action of . The
method is then generalized and explicitly applied to the case that is
the quantum group . A preliminary study of the status of deforming
maps at the representation level shows in particular that `deformed' Fock
representations induced by a compact can be interpreted as standard
`undeformed' Fock representations describing particles with ordinary Bose or
Fermi statistics.Comment: Latex file, 26 pages, no figures. Extended changes. Final Version to
appear in J. Math. Phy
Modeling Expertise in Assistive Navigation Interfaces for Blind People
Evaluating the impact of expertise and route knowledge on task performance can guide the design of intelligent and adaptive navigation interfaces. Expertise has been relatively unexplored in the context of assistive indoor navigation interfaces for blind people. To quantify the complex relationship between the user's walking patterns, route learning, and adaptation to the interface, we conducted a study with 8 blind participants. The participants repeated a set of navigation tasks while using a smartphone-based turn-by-turn navigation guidance app. The results demonstrate the gradual evolution of user skill and knowledge throughout the route repetitions, significantly impacting the task completion time. In addition to the exploratory analysis, we take a step towards tailoring the navigation interface to the user's needs by proposing a personalized recurrent neural net work-based behavior model for expertise level classification
The Gervais-Neveu-Felder equation for the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra
Using a contraction procedure, we construct a twist operator that satisfies a
shifted cocycle condition, and leads to the Jordanian quasi-Hopf U_{h;y}(sl(2))
algebra. The corresponding universal matrix obeys a
Gervais-Neveu-Felder equation associated with the U_{h;y}(sl(2)) algebra. For a
class of representations, the dynamical Yang-Baxter equation may be expressed
as a compatibility condition for the algebra of the Lax operators.Comment: Latex, 9 pages, no figure
h-deformation of Gr(2)
The -deformation of functions on the Grassmann matrix group is
presented via a contraction of . As an interesting point, we have seen
that, in the case of the -deformation, both R-matrices of and
are the same
Non-standard quantum so(3,2) and its contractions
A full (triangular) quantum deformation of so(3,2) is presented by
considering this algebra as the conformal algebra of the 2+1 dimensional
Minkowskian spacetime. Non-relativistic contractions are analysed and used to
obtain quantum Hopf structures for the conformal algebras of the 2+1 Galilean
and Carroll spacetimes. Relations between the latter and the null-plane quantum
Poincar\'e algebra are studied.Comment: 9 pages, LaTe
Integrable deformations of oscillator chains from quantum algebras
A family of completely integrable nonlinear deformations of systems of N
harmonic oscillators are constructed from the non-standard quantum deformation
of the sl(2,R) algebra. Explicit expressions for all the associated integrals
of motion are given, and the long-range nature of the interactions introduced
by the deformation is shown to be linked to the underlying coalgebra structure.
Separability and superintegrability properties of such systems are analysed,
and their connection with classical angular momentum chains is used to
construct a non-standard integrable deformation of the XXX hyperbolic Gaudin
system.Comment: 15 pages, LaTe
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 user’s or group of user’s 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
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
Universal --matrices for non-standard (1+1) quantum groups
A universal quasitriangular --matrix for the non-standard quantum (1+1)
Poincar\'e algebra is deduced by imposing analyticity in the
deformation parameter . A family of ``quantum graded contractions"
of the algebra is obtained; this set of
quantum algebras contains as Hopf subalgebras with two primitive translations
quantum analogues of the two dimensional Euclidean, Poincar\'e and Galilei
algebras enlarged with dilations. Universal --matrices
for these quantum Weyl algebras and their associated quantum groups are
constructed.Comment: 12 pages, LaTeX
Classification of the quantum deformation of the superalgebra
We present a classification of the possible quantum deformations of the
supergroup and its Lie superalgebra . In each case, the
(super)commutation relations and the Hopf structures are explicitly computed.
For each matrix, one finds two inequivalent coproducts whether one chooses
an unbraided or a braided framework while the corresponding structures are
isomorphic as algebras. In the braided case, one recovers the classical algebra
for suitable limits of the deformation parameters but this is no
longer true in the unbraided case.Comment: 23p LaTeX2e Document - packages amsfonts,subeqn - misprints and
errors corrected, one section adde
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