Generalized triply special relativity models and their classical limit

Triply Special Relativity is a deformation of Special Relativity based on three fundamental parameters that describes a noncommutative geometry on a curved space-time, preserving the Lorentz invariance and the principle of relativity. Its symmetries are generated by a 14-parameter nonlinear algebra. In this paper, we discuss a generalization of the original model and construct its realizations on a canonical phase space. We also investigate in more detail its classical limit, obtained by replacing the commutators by Poisson brackets.