Geodesic
Structure of some compact quantum semigroups
Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 2, pp. 18-26 Cet article a éte moissonné depuis la source Math-Net.Ru

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We show that the main results of multuplicative unitary theory do not hold for compact quantum semigroups and give examples. We suggest a new method to provide compact quantum semigroup structure by the use of pentagon equation, which gives a generalization of multiplicative unitary theory. 
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M. A. Aukhadiev. Structure of some compact quantum semigroups. Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 2, pp. 18-26. http://geodesic.mathdoc.fr/item/VMJ_2013_15_2_a2/

[1] Tannaka T., “Uber den Dualitatssatz der nichtkommutativen topologischen Gruppen”, Tohoku Math. J., 45 (1939), 1–12

[2] Krein M. G., “Printsip dvoistvennosti dlya bikompaktnoi gruppy i kvadratnoi blok-algebry”, Dokl. AN SSSR, 69 (1949), 725–728 | MR

[3] Takesaki M., “Duality and von Neumann algebras”, Bull. Amer. Math. Soc., 77:4 (1971), 553–557 | DOI | MR | Zbl

[4] Woronowicz S. L., “Compact quantum groups”, Symétries quantiques (Les Houches, 1995), North-Holland, Amsterdam, 1998, 845–884 | MR | Zbl

[5] Baaj S., Skandalis G., “Unitaires multiplicatifs et dualité pour les produits croisés de $C^*$-algébres”, Ann. Sci. Ecole. Norm. Sup. Ser. 4, 26:4 (1993), 425–488 | MR | Zbl

[6] Maes A., Van Daele A., “Notes on Compact Quantum Groups”, Nieuw Arch. Wisk. Ser. 4, 16:1–2 (1998), 73–112 | MR | Zbl

[7] Aukhadiev M. A., Grigoryan S. A., Lipacheva E. V., “Kompaktnaya kvantovaya polugruppa, porozhdennaya izometriei”, Izv. vuzov. Matematika, 2011, no. 10, 89–93 | MR | Zbl