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arXiv · 1504.00407

Quantum semigroups generated by locally compact semigroups

Marat A. Aukhadiev·Yulia N. Kuznetsova
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Abstract

Let $S$ be a subsemigroup of a second countable locally compact group $G$, such that $S^{-1}S=G$. We consider the $C^*$-algebra $C^*_\delta(S)$ generated by the operators of translation by all elements of $S$ in $L^2(S)$. We show that this algebra admits a comultiplication which turns it into a compact quantum semigroup. The same is proved for the von Neumann algebra $VN(S)$ generated by $C^*_\delta(S)$.

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Marat A. Aukhadiev, Yulia N. Kuznetsova. 2015-04-01. Quantum semigroups generated by locally compact semigroups. https://doi.org/10.1215/ijm/1552442656

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