THE POINCARE LIMIT IN 2+1 DIMENSIONAL QUANTUM DESITTER GRAVITY

The quantum traces algebra for the 2 + 1 Poincare gravity in first order formalism is explicitly constructed by contracting the corresponding traces algebra of the de Sitter gravity. Unbounded representations of the latter, in the case LAMBDA < 0, are constructed in terms of an underlying SU(1, 1) algebra. Unfortunately, these representations do not possess a well defined Poincare limit. Nevertheless an explicit realization of the Poincare traces algebra is constructed in terms of two pairs of canonical variables.