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2018 Quantum semigroups generated by locally compact semigroups
M. A. Aukhadiev, Y. N. Kuznetsova
Illinois J. Math. 62(1-4): 41-60 (2018). DOI: 10.1215/ijm/1552442656


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 $\operatorname{VN}(S)$ generated by $C^{*}_{\delta }(S)$.


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M. A. Aukhadiev. Y. N. Kuznetsova. "Quantum semigroups generated by locally compact semigroups." Illinois J. Math. 62 (1-4) 41 - 60, 2018.


Received: 11 September 2015; Revised: 14 July 2018; Published: 2018
First available in Project Euclid: 13 March 2019

zbMATH: 07036780
MathSciNet: MR3922410
Digital Object Identifier: 10.1215/ijm/1552442656

Primary: 16T10, 20G42, 22A20, 81R15

Rights: Copyright © 2018 University of Illinois at Urbana-Champaign