Geodesic
An example of a cosimple and co-commutative compact quantum semigroup
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2018), pp. 69-76.

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We construct a co-multiplication on the semigroup Cuntz–Toeplitz $C^*$-algebra and obtain a compact quantum semigroup structure on this algebra. We show that the unique proper ideal of the Cuntz–Toeplitz algebra is not a coideal of the compact quantum semigroup. Thus, the compact quantum semigroup is a cosimple quantum semigroup.
Keywords: $C^*$-algebra, inverse semigroup, semigroup algebra, Wagner representation, compact quantum semigroup, Cuntz algebra, Cuntz semigroup, Cuntz–Toeplitz algebra. 
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E. V. Lipacheva. An example of a cosimple and co-commutative compact quantum semigroup. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2018), pp. 69-76. http://geodesic.mathdoc.fr/item/IVM_2018_2_a6/

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