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arXiv · 1706.10138

Group-like projections for locally compact quantum groups

Ramin Faal·Paweł Kasprzak
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Abstract

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 $\mathbb{G}$.

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Ramin Faal, Paweł Kasprzak. 2018-01-08. Group-like projections for locally compact quantum groups. https://arxiv.org/abs/1706.10138

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