De Sitter space as an arena for doubly special relativity

We show that Doubly Special Relativity (DSR) can be viewed as a theory with energy–momentum space being the four-dimensional de Sitter space. Different formulations (bases) of the DSR theory considered so far can be therefore understood as different coordinate systems on this space. The emerging geometrical picture makes it possible to understand the universality of the non-commutative structure of space–time of doubly special relativity. Moreover, it suggests how to construct the most natural DSR basis, which turns out to be the bicrossproduct basis.