Why is it interesting?

Given the current picture of an increasingly expanding universe, it may very well be the case that future generations of students first learn about the de Sitter and the Newton-Hooke groups, while the Poincaré and the Galilei groups will be considered to be nothing but historical aberrations. Symmetries in Fundamental Physics by Kurt Sundermeyer

Layman

The symmetry group that we use when we only consider the principle that all inertial frames of reference should be the same, called Galilean relativity, is the Galilean group.

If we add to this principle that there should be an invariant velocity $c$, we end up with special relativity and the corresponding symmetry group is the Poincare group.

If we then add a second principle that says there should be an invariant length scale $R$ (= an invariant energy scale $\Lambda$), the deSitter group is the group that we must use.

The deSitter group becomes the Poincare group in the contraction limit $R \rightarrow \infty$, where $R$ is the so-called deSitter radius. Oftentimes, people prefer to work with the cosmological constant $ \Lambda \propto \frac{1}{R^2}$ instead. Analogously, the Poincare group becomes the Galilean group in the $c \rightarrow \infty$ limit.

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