We investigate a nonlinear realization of the Lorentz transformation defined in 4-dimensional spacetime, and the corresponding\r\ninvariant interval. This new interval is not a quadratic form in the standardMinkowski spacetime, then we search for a description\r\nwhere it becomes a quadratic form in an infinite dimensional vector space. In this extended space, we show how to generate two\r\nclasses of nonlinear transformations, which form a group and interpret the non-linear transformation as compatible relations\r\nbetween atlas of a Lyra manifold.
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