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Original Articles

PENTAGON EQUATION AND MATRIX BIALGEBRAS

Pages 2627-2650
Received 01 Jan 2000
Published online: 16 Aug 2006
 
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We classify coproducts on matrix algebra in terms of solutions to some modification of pentagon equation. The construction of Baaj and Skandalis describing finite dimensional unitary solutions of the pentagon equation is extended to the non-unitary case. We establish the relation between Hopf-Galois algebras and solutions to the modified pentagon equation.

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ACKNOWLEDGMENT

The work was started during my visit of Macquarie University (Sydney, Australia) and was completed in Max-Planck-Institut für Mathematik (Bonn, Germany). I would like to thank these institutions for hospitality and inspiring atmosphere. Special thanks to Prof. Ross Street who pointed out to me the references [7] Skandalis, Georges. 1990. Operator algebras and duality. Proceedings of the International Congress of Mathematicians. 1990, Kyoto. Vol. II, pp.9971009. Math. Soc. Japan, Tokyo, 1991 [Google Scholar], [1] Baaj, Saad and Skandalis, Georges. 1993. Unitaires multiplicatifs et dualite pour les produits croises de C*-algebres. Ann. Sci. Ecole Norm. Sup. (4), 26(4): 425488. [Crossref] [Google Scholar] and explained his own work [8] Street, Ross. 1998. Fusion operators and cocycloids in monoidal categories. Appl. Categ. Structures, 6(2): 177191. [Crossref], [Web of Science ®] [Google Scholar].

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