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...

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 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.

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.

Classifying bicrossed products of two Sweedler's Hopf algebras

Costel-Gabriel Bontea (2014)

Czechoslovak Mathematical Journal

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We continue the study started recently by Agore, Bontea and Militaru in “Classifying bicrossed products of Hopf algebras” (2014), by describing and classifying all Hopf algebras E that factorize through two Sweedler’s Hopf algebras. Equivalently, we classify all bicrossed products H 4 ⋈ H 4 . There are three steps in our approach. First, we explicitly describe the set of all matched pairs ( H 4 , H 4 , ▹ , ◃ ) by proving that, with the exception of the trivial pair, this set is parameterized by the ground field...