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 $\Gamma$ equipped with a $2$-cocycle $\Psi :\hat{\Gamma }\times \hat{\Gamma }\to \mathbb{C}$. 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 ${\mathbb{G}}^{\Psi }$.

arXiv comment37 pages. v3: minor changes. To appear in Letters in Mathematical Physics

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