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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.

17B37Quantum groups and related deformations
46L85Noncommutative topology
46L87Noncommutative differential geometry
81R50Quantum groups and related algebraic methods in quantum theory
16W30Hopf algebras (associative rings and algebras) (MSC2000)
Full Text: DOI
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