Kappa Snyder deformations of Minkowski spacetime, realizations, and Hopf algebra

We present Lie-algebraic deformations of Minkowski space with undeformed Poincaré algebra. These deformations interpolate between Snyder and $\kappa$-Minkowski space. We find realizations of noncommutative coordinates in terms of commutative coordinates and derivatives. By introducing modules, it is shown that, although deformed and undeformed structures are not isomorphic at the level of vector spaces, they are isomorphic at the level of Hopf-algebraic action on corresponding modules. Invariants and tensors with respect to Lorentz algebra are discussed. A general mapping from $\kappa$-deformed Snyder to Snyder space is constructed. The deformed Leibniz rule, the Hopf structure, and the star product are found. Special cases, particularly Snyder and $\kappa$-Minkowski in Maggiore-type realizations, are discussed. The same generalized Hopf-algebraic structures are considered as well in the case of an arbitrary allowable kind of realization, and results are given perturbatively up to second order in deformation parameters.