Some Examples of Bicrossed Products with the Rapid Decay Property

Abstract

We consider bicrossed products obtained by twisting compact semi-direct products by a suitable finite subgroup. Under some restriction, we give a practical criterion for the discrete dual of such bicrossed products to have the rapid decay property (property (RD)). Using this theory, we construct some examples of discrete quantum groups with (RD) but do not grow polynomially. Further examples that do not satisfy the hypothesis of our main result are also constructed.