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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 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
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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.
Received: 11.11.2016
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, Volume 62, Issue 2, Pages 62–68
DOI: https://doi.org/10.3103/S1066369X1802007X
Bibliographic databases:
Document Type: Article
UDC: 512.667
Language: Russian
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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\issue 2
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    References:27
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