The Yang-Baxter and pentagon equation

A. Van Daele; S. Van Keer

Displaying similar documents to “The Yang-Baxter and pentagon equation”

More examples of invariance under twisting

Florin Panaite (2012)

Czechoslovak Mathematical Journal

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The so-called “invariance under twisting” for twisted tensor products of algebras is a result stating that, if we start with a twisted tensor product, under certain circumstances we can “deform” the twisting map and we obtain a new twisted tensor product, isomorphic to the given one. It was proved before that a number of independent and previously unrelated results from Hopf algebra theory are particular cases of this theorem. In this article we show that some more results from literature...

Coalgebra deformations of bialgebras by Harrison cocycles, copairings of Hopf algebras and double crosscoproducts.

Caenepeel, S., Dăscălescu, S., Militaru, G., Panaite, F. (1997)

Bulletin of the Belgian Mathematical Society - Simon Stevin

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Twisted quantum doubles.

Fukuda, Daijiro, Kuga, Ken'ichi (2004)

International Journal of Mathematics and Mathematical Sciences

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On complements and the factorization problem of Hopf algebras

Sebastian Burciu (2011)

Open Mathematics

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Two new results concerning complements in a semisimple Hopf algebra are proved. They extend some well-known results from group theory. The uniqueness of a Krull-Schmidt-Remak type decomposition is proved for semisimple completely reducible Hopf algebras.

The coribbon structures of some finite dimensional braided Hopf algebras generated by 2×2-matrix coalgebras

Michihisa Wakui (2003)

Banach Center Publications

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We determine the coribbon structures of some finite dimensional braided Hopf algebras generated by 2×2-matrix coalgebras constructed by S. Suzuki. As a consequence, we see that such a Hopf algebra has a coribbon structure if and only if it is of Kac-Paljutkin type.

The strong Morita equivalence for coactions of a finite-dimensional C-Hopf algebra on unital C-algebras

Kazunori Kodaka, Tamotsu Teruya (2015)

Studia Mathematica

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Following Jansen and Waldmann, and Kajiwara and Watatani, we introduce notions of coactions of a finite-dimensional C*-Hopf algebra on a Hilbert C*-bimodule of finite type in the sense of Kajiwara and Watatani and define their crossed product. We investigate their basic properties and show that the strong Morita equivalence for coactions preserves the Rokhlin property for coactions of a finite-dimensional C*-Hopf algebra on unital C*-algebras.

Cosemisimple Hopf algebras with antipode of arbitrary finite order.

Bichon, Julien (2002)

The New York Journal of Mathematics [electronic only]

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Hopf structures on the Borel subalgebra of $s l (2)$

Ogievetsky, O.

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On Singer's algebra and coalgebra structures

Luciano A. Lomonaco (2006)

Bollettino dell'Unione Matematica Italiana

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Recently W. M. Singer has introduced the notion of algebra with coproducts (and the dual notion of coalgebra with products) by somehow weakening the notion of Hopf algebra (see [6]). In this paper we consider certain algebras of invariants and show that they are, in fact, further examples of algebras with coproducts and coalgebras with products. Moreover, we discuss the close relation between such algebras and the structures considered in Singer's paper.