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An Example of a Cosimple and Co-Commutative Compact Quantum Semigroup

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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 co-ideal of the compact quantum semigroup. Thus, the compact quantum semigroup is a co-simple quantum semigroup.

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Authors and Affiliations

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

    E. V. Lipacheva

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  1. E. V. Lipacheva
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Correspondence to E. V. Lipacheva.

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Original Russian Text © E.V. Lipacheva, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 2, pp. 69–76.

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Lipacheva, E.V. An Example of a Cosimple and Co-Commutative Compact Quantum Semigroup. Russ Math. 62, 62–68 (2018). https://doi.org/10.3103/S1066369X1802007X

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