Hopf structures on the Borel subalgebra of
Ogievetsky, O.
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Ogievetsky, O.
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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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Fukuda, Daijiro, Kuga, Ken'ichi (2004)
International Journal of Mathematics and Mathematical Sciences
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Cheng, Dongming (2010)
International Journal of Mathematics and Mathematical Sciences
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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.
Natale, Sonia (2003)
AMA. Algebra Montpellier Announcements [electronic only]
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Bichon, Julien (2002)
The New York Journal of Mathematics [electronic only]
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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. ...
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.
Sommerhäuser, Yorck (1996)
The New York Journal of Mathematics [electronic only]
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A. van Daele (1997)
Banach Center Publications
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We define a category containing the discrete quantum groups (and hence the discrete groups and the duals of compact groups) and the compact quantum groups (and hence the compact groups and the duals of discrete groups). The dual of an object can be defined within the same category and we have a biduality theorem. This theory extends the duality between compact quantum groups and discrete quantum groups (and hence the one between compact abelian groups and discrete abelian groups). The...