Convolution semigroups on Rieffel deformations of locally compact quantum groups

Consider a locally compact quantum group \(\mathbb {G}\) with a closed classical abelian subgroup \(\Gamma \) equipped with a 2-cocycle \(\Psi :\hat{\Gamma }\times \hat{\Gamma }\rightarrow \mathbb {C}\). We study in detail the associated Rieffel deformation \(\mathbb {G}^{\Psi }\) and establish a canonical correspondence between \(\Gamma \)-invariant convolution semigroups of states on \(\mathbb {G}\) and on \(\mathbb {G}^{\Psi }\).