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Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach. (English) Zbl 1411.81119
Summary: We consider new abelian twists of Poincaré algebra describing nonsymmetric generalization of the ones given in [the first and the last author, ibid. 633, No. 1, 116–124 (2006; Zbl 1247.81216)], which lead to the class of Lie-deformed quantum Minkowski spaces. We apply corresponding twist quantization in two ways: as generating quantum Poincaré-Hopf algebra providing quantum Poincare symmetries, and by considering the quantization which provides Hopf algebroid describing class of quantum relativistic phase spaces with built-in quantum Poincaré covariance. If we assume that Lorentz generators are orbital, i.e., do not describe spin degrees of freedom, one can embed the considered generalized phase spaces into the ones describing the quantum-deformed Heisenberg algebras.

MSC:
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
58B32 Geometry of quantum groups
17B37 Quantum groups (quantized enveloping algebras) and related deformations
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