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Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 2, Pages 69–76 (Mi ivm9331)  

An example of a cosimple and co-commutative compact quantum semigroup

E. V. Lipacheva

Kazan State Power Engineering University, 51 Krasnosel’skaya str., Kazan, 420066 Russia

Abstract: 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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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:2, 62–68

Bibliographic databases:

UDC: 512.667
Received: 11.11.2016

Citation: E. V. Lipacheva, “An example of a cosimple and co-commutative compact quantum semigroup”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 2, 69–76; Russian Math. (Iz. VUZ), 62:2 (2018), 62–68

Citation in format AMSBIB
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\paper An example of a cosimple and co-commutative compact quantum semigroup
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2018
\issue 2
\pages 69--76
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\jour Russian Math. (Iz. VUZ)
\yr 2018
\vol 62
\issue 2
\pages 62--68
\crossref{https://doi.org/10.3103/S1066369X1802007X}
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