Journal of Operator Theory

Volume 80, Issue 1, Summer 2018 pp. 153-166.

Group-like projections for locally compact quantum groups

Authors: Ramin Faal (1) and Pawel Kasprzak (2)
Author institution: 1) Department of Pure Mathematics, Ferdowsi University of Mashhad, Iran (2) Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Poland

Summary: Let $\mathbb{G}$ be a locally compact quantum group. We give a 1-1 correspondence between group-like projections in $L^\infty(\mathbb{G})$ preserved by the scaling group and idempotent states on the dual quantum group $\widehat{\mathbb{G}}$. As a byproduct we give a simple proof that normal integrable coideals in $L^\infty(\mathbb{G})$ which are preserved by the scaling group are in 1-1 correspondence with compact quantum subgroups of $\mathbb{G}$.

DOI: http://dx.doi.org/10.7900/jot.2017jul12.2166
Keywords: locally compact quantum group, group-like projections, idempotent states

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