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Convolution semigroups on Rieffel deformations of locally compact quantum groups

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Abstract

Consider a locally compact quantum group \(\mathbb {G}\) with a closed classical abelian subgroup \(\Gamma \) equipped with a 2-cocycle \(\Psi :\hat{\Gamma }\times \hat{\Gamma }\rightarrow \mathbb {C}\). 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 \(\mathbb {G}^{\Psi }\).

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Authors and Affiliations

  1. Institute of Mathematics of the Polish Academy of Sciences, ul. Śniadeckich 8, 00-656, Warszawa, Poland

    Adam Skalski

  2. Department of Mathematics, University of Haifa, 3103301, Haifa, Israel

    Ami Viselter

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  1. Adam Skalski
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  2. Ami Viselter
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Correspondence to Adam Skalski.

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Skalski, A., Viselter, A. Convolution semigroups on Rieffel deformations of locally compact quantum groups. Lett Math Phys 114, 52 (2024). https://doi.org/10.1007/s11005-024-01797-w

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