Algebras Graded by Discrete Doi–Hopf Data and the Drinfeld Double of a Hopf Group-Coalgebra
نویسندگان
چکیده
منابع مشابه
Coalgebra deformations of bialgebras by Harrison cocycles, copairings of Hopf algebras and double crosscoproducts
We study how the comultiplication on a Hopf algebra can be modified in such a way that the new comultiplication together with the original multiplication and a suitable antipode gives a new Hopf algebra. To this end, we have to study Harrison type cocycles, and it turns out that there is a relation with the Yang-Baxter equation. The construction is applied to deform the coalgebra structure on t...
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Cocycle Deformations for Hopf Algebras with a Coalgebra Projection
In this paper we study Hopf algebras with a coalgebra projection A ∼= R#ξH and their deformations by an H-bilinear cocycle. If γ is a cocycle for A, then γ can be restricted to a cocycle γR for R, and A γ ∼= RR#ξγH. As examples, we consider liftings of B(V )#K[Γ] where Γ is a finite abelian group, V is a quantum plane and B(V ) is its Nichols algebra, and explicitly construct the cocycle which ...
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Quantum groups, from a mathematical point of view, may be introduced by making emphasis on their q−deformed enveloping algebra aspects [1,2], which leads to the quantized enveloping algebras, or by making emphasis in the R−matrix formalism that describes the deformed group algebra. Also, they are mathematically well defined in the framework of Hopf algebra [3]. Quantum groups provide an interes...
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2011
ISSN: 1386-923X,1572-9079
DOI: 10.1007/s10468-011-9300-8