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The Yang model is an example of noncommutative geometry on a background spacetime of constant curvature. We discuss the Hermitian realizations of its associated algebra on phase space in a perturbative expansion up to sixth order. We also discuss its realizations on extended phase spaces, that include additional tensorial and/or vectorial degrees or freedom. [ABSTRACT FROM AUTHOR]

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 o ˆ (1 , 5) algebras. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of Very Special Relativity is to show that the subgroup of the Poincaré group is sufficient to describe the spacetime symmetries of the so far observed physical phenomena. A deformation of such group, called , was later introduced. In the present work, we present a novel non-commutative spacetime structure, underlying the , that allows us to construct explicitly the generators of the group. Exploiting the Darboux map technique, we then construct a point particle Lagrangian that lives in the non-commutative phase space proposed by us. [Copyright &y& Elsevier]