Towards new relativistic doubly kappa-deformed D = 4 quantum phase spaces

We propose new noncommutative models of quantum phase spaces, containing a pair of κ-deformed Poincaré algebras, with two independent double (κ,κ~)-deformations in space-time and four-momenta sectors. The first such quantum phase space can be obtained by contractions M,R→∞ of recently introduced doubly κ-deformed (κ,κ~)-Yang models, with the parameters M, R describing inverse space-time and four-momenta curvatures and constant four-vectors aμ,bμ determining nine types of (κ,κ~)-deformations. The second considered model is provided by the nonlinear doubly κ-deformed TSR algebra spanned by 14 coset o^(1,5)/o^(2) generators. The basic algebraic difference between the two models is the following: the first one, described by o^(1,5) Lie algebra can be supplemented by the Hopf algebra structure, while the second model contains the quantum phase space commutators [x^μ,q^ν], with the standard numerical iħημν term; therefore, it describes the quantum-deformed Heisenberg algebra relations which cannot be equipped with the Hopf algebra.