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Acta Applicandae Mathematicae

, Volume 101, Issue 1–3, pp 85–104 | Cite as

Noncommutative Dynamical Models with Quantum Symmetries

  • Antoine Dutriaux
  • Dimitri Gurevich
Article

Abstract

We define dynamical models on the q-Minkowski space algebra (which is a particular case of the Reflection Equation Algebra) as deformations (quantizations) of dynamical models with rotational symmetries, and we find their integrals. In particular, we introduce a q-analog of the Runge-Lenz vector and a q-analog of the dynamics in space-time with a spherically symmetric metric.

Keywords

q-Minkowski space algebra (Modified) reflection equation algebra Quantum group Cayley-Hamilton identity Verma modules Integrals of dynamics 

Mathematics Subject Classification (2000)

17B37 81R12 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.USTVUniversité de ValenciennesValenciennesFrance

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