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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:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
46L85 Noncommutative topology
46L87 Noncommutative differential geometry
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
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References:

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