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We use the mathematical framework of loop quantum gravity (LQG) to study thequantization of three dimensional (Riemannian) gravity with positivecosmological constant (Lambda>0). We show that the usual regularizationtechniques (successful in the Lambda=0 case and widely applied in fourdimensional LQG) lead to a deformation of the classical constraint algebra (oranomaly) proportional to the local strength of the curvature squared. We arguethat this is an unavoidable consequence of the non-local nature of generalizedconnections.

On the regularization of the constraints algebra of Quantum Gravity in 2+1 dimensions with non-vanishing cosmological constant