Forms of Certain Hopf Algebras.
D.E. Radford, E.J. Taft, R.L. Wilson (1975)
Manuscripta mathematica
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D.E. Radford, E.J. Taft, R.L. Wilson (1975)
Manuscripta mathematica
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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.
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.
Jean Ludwig (1979/80)
Manuscripta mathematica
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Natale, Sonia (2003)
AMA. Algebra Montpellier Announcements [electronic only]
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Caenepeel, S., Dăscălescu, S., Militaru, G., Panaite, F. (1997)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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Bichon, Julien (2002)
The New York Journal of Mathematics [electronic only]
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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.
Thomas Timmermann, Alfons Van Daele (2015)
Banach Center Publications
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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...
José N. Alonso Alvarez, José Manuel Fernández Vilaboa, Ramón González Rodríguez (2001)
Publicacions Matemàtiques
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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. ...
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 that factorize through two Sweedler’s Hopf algebras. Equivalently, we classify all bicrossed products . There are three steps in our approach. First, we explicitly describe the set of all matched pairs by proving that, with the exception of the trivial pair, this set is parameterized by the ground field...
Xiaofan Zhao, Xiaohui Zhang (2016)
Colloquium Mathematicae
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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.
Alfons Van Daele, Shuanhong Wang (2012)
Banach Center Publications
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Let G be a finite group. Consider the algebra A of all complex functions on G (with pointwise product). Define a coproduct Δ on A by Δ(f)(p,q) = f(pq) where f ∈ A and p,q ∈ G. Then (A,Δ) is a Hopf algebra. If G is only a groupoid, so that the product of two elements is not always defined, one still can consider A and define Δ(f)(p,q) as above when pq is defined. If we let Δ(f)(p,q) = 0 otherwise, we still get a coproduct on A, but Δ(1) will no longer be the identity in A ⊗ A....
Sterling K. Berberian (1983)
Mathematische Zeitschrift
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Aleksandar T. Lipkovski (2002)
Visual Mathematics
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W. Żelazko (2005)
Studia Mathematica
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We prove that a real or complex F-algebra has all left and right ideals closed if and only if it is noetherian.