From Snyder space-times to doubly κ-dependent Yang quantum phase spaces and their generalizations

We propose the doubly κ-dependent Yang quantum phase space which describes the generalization of D=4 Yang model. We postulate that such model is covariant under the generalized Born map, what permits to derive this new model from the earlier proposed κ-Snyder model. Our model of D=4 relativistic Yang quantum phase space depends on five deformation parameters which form two Born map-related dimensionful pairs: (M,R) specifying the standard Yang model and (κ,κ˜) characterizing the Born-dual κ-dependence of quantum space-time and quantum fourmomenta sectors; fifth parameter ρ is dimensionless and Born-selfdual. In the last section, we propose the Kaluza-Klein generalization of D=4 Yang model and the new quantum Yang models described algebraically by quantum-deformed oˆ(1,5) algebras.