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The Lorentz transfomation is derived in 5D flat pseudo-complex affine spaceor TT Space. The TT space or pseudo-Complex space accomodates oneuncompactified time-like extra dimension. It is shown that the maximumallowable speed for particles living in TT space exceeds the speed of light, c,the absolute speed of the Minkowski space.

Lorentz Transformation in Flat 5D Complex-Hyperbolic Space