Two one-parameter families of twists providing kappa-Minkowski * -product deformed spacetime are considered: Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two perspectives. The first one is the Hopf module algebra point of view, which is strictly related with Drinfelds twisting tensor technique. The other one relies on an appropriate extension of deformed realizations of nondeformed Lorentz algebra by the quantum Minkowski algebra. This extension turns out to be de Sitter Lie algebra. We show the way both approaches are related. The second path allows us to calculate deformed dispersion relations for toy models ensuing from different twist parameters. In the Abelian case one recovers kappa-Poincare dispersion relations having numerous applications in doubly special relativity. Jordanian twists provide a new type of dispersion relations which in the minimal case (related to Weyl-Poincare algebra) takes an energy-dependent linear mass deformation form.
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