Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces

Abstract

We study the general deformed conformal-Poincare (Galilean) symmetries consistent with relativistic (nonrelativistic) canonical noncommutative spaces. In either case we obtain deformed generators, containing arbitrary free parameters, which close to yield new algebraic structures. We show that a particular choice of these parameters reproduces the undeformed algebra. The modified coproduct rules and the associated Hopf algebra are also obtained. Finally, we show that for the choice of parameters leading to the undeformed algebra, the deformations are represented by twist functions.

arXiv comment9 pages, LaTeX, shortened, version appearing in Phys. Rev. D

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Cited by in corpus (10)

• Topics in Noncommutative Geometry Inspired Physics
• Remarks on the Noncommutative Gravitational Quantum Well
• Noncommutative oscillator, symmetry and Landau problem
• Exotic galilean symmetry and non-commutative mechanics
• Dynamical symmetries in noncommutative theories
• The Noncommutative Doplicher-Fredenhagen-Roberts-Amorim Space
• Particle Dynamics and Lie-algebraic type of Non-commutativity of space-time
• Inverse square problem and so(2,1) symmetry in noncommutative space
• Theories on noncommutative spaces and deformed symmetries
• Aspects of noncommutativity in field theory, strings and membranes