κ-Minkowski spacetime as the result of Jordanian twist deformation

Two one-parameter families of twists providing κ−Minkowski ∗−product deformed spacetime are considered: Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two perspectives. First one is the Hopf module algebra point of view, which is strictly related with Drinfeld’s twisting tensor technique. An other one relies on an appropriate extension of deformed realizations of non-deformed 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 relation for toy models ensuing from different twist parameters. In the Abelian case one amazingly recovers κ−Poincare dispersion relation having numerous applications in DSR. Jordanian twists provide new type of dispersion relations which in the minimal case (related with Weyl-Poincare algebra) takes energy-dependent linear mass deformation formula. ∗e-mail: [email protected] †e-mail: [email protected]