Half-sided modular inclusion and the construction of the Poincare group

In this note we will give a construction of the Poincare group out of the modular groups of the wedge algebras provided the groups act on the algebra of every double cone like the associated Lorentz boosts. This construction will use the concept of half-sided modular inclusions instead of the first and second cohomology of the Poincare group as used by Brunetti, Guide and Longo. By our method we obtain directly the Poincare group and not its covering group.