Convolution semigroups on Rieffel deformations of locally compact quantum groups

Abstract

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