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q-deformed Poincaré algebra. (English) Zbl 0849.17011
Summary: The q-differential calculus for the q-Minkowski space is developed. The algebra of the q-derivatives with the q-Lorentz generators is found giving the q-deformation of the Poincaré algebra. The reality structure of the q-Poincaré algebra is given. The reality structure of the q-differentials is also found. The real Laplacian is constructed. Finally the comultiplication, counit and antipode for the q-Poincaré algebra are obtained making it a Hopf algebra.

MSC:
17B37Quantum groups and related deformations
46L85Noncommutative topology
46L87Noncommutative differential geometry
81R50Quantum groups and related algebraic methods in quantum theory
16W30Hopf algebras (assoc. rings and algebras) (MSC2000)
References:
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