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

Caenepeel, S.; Dăscălescu, S.; Militaru, G.; Panaite, F.

The search session has expired. Please query the service again.

Displaying similar documents to “Coalgebra deformations of bialgebras by Harrison cocycles, copairings of Hopf algebras and double crosscoproducts.”

Smash (co)products and skew pairings.

José N. Alonso Alvarez, José Manuel Fernández Vilaboa, Ramón González Rodríguez (2001)

Publicacions Matemàtiques

Similarity:

Let τ be an invertible skew pairing on (B,H) where B and H are Hopf algebras in a symmetric monoidal category C with (co)equalizers. Assume that H is quasitriangular. Then we obtain a new algebra structure such that B is a Hopf algebra in the braided category γD and there exists a Hopf algebra isomorphism w: B ∞ H → B [×] H in C, where B ∞ H is a Hopf algebra with (co)algebra structure the smash (co)product and B [×] H is the Hopf algebra defined by Doi and Takeuchi. ...

On complements and the factorization problem of Hopf algebras

Sebastian Burciu (2011)

Open Mathematics

Similarity:

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

Similarity:

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.

Lazy 2-cocycles over monoidal Hom-Hopf algebras

Xiaofan Zhao, Xiaohui Zhang (2016)

Colloquium Mathematicae

Similarity:

We introduce the notion of a lazy 2-cocycle over a monoidal Hom-Hopf algebra and determine all lazy 2-cocycles for a class of monoidal Hom-Hopf algebras. We also study the extension of lazy 2-cocycles to a Radford Hom-biproduct.

On semisimple Hopf algebras of low dimension.

Natale, Sonia (2003)

AMA. Algebra Montpellier Announcements [electronic only]

Similarity:

Classifying bicrossed products of two Sweedler's Hopf algebras

Costel-Gabriel Bontea (2014)

Czechoslovak Mathematical Journal

Similarity:

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...

Cosemisimple Hopf algebras with antipode of arbitrary finite order.

Bichon, Julien (2002)

The New York Journal of Mathematics [electronic only]

Similarity:

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

Kazunori Kodaka, Tamotsu Teruya (2015)

Studia Mathematica

Similarity:

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.

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

Ogievetsky, O.

Similarity:

Twisted quantum doubles.

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

International Journal of Mathematics and Mathematical Sciences

Similarity:

Multiplier Hopf algebroids arising from weak multiplier Hopf algebras

Thomas Timmermann, Alfons Van Daele (2015)

Banach Center Publications

Similarity:

It is well-known that any weak Hopf algebra gives rise to a Hopf algebroid. Moreover it is possible to characterize those Hopf algebroids that arise in this way. Recently, the notion of a weak Hopf algebra has been extended to the case of algebras without identity. This led to the theory of weak multiplier Hopf algebras. Similarly also the theory of Hopf algebroids was recently developed for algebras without identity. They are called multiplier Hopf algebroids. Then...