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

We propose the doubly K-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 K-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 (K, K) characterizing the Born-dual K-dependence of quantum spacetime and quantum fourmomenta sectors; fifth parameter p 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 & ocirc;(1, 5) algebras.