Bosonization for dual quasi-bialgebras and preantipode

Details Bosonization for dual quasi-bialgebras and preantipode Bosonization for dual quasi-bialgebras and preantipode

2011-11-18

arxiv.org/abs/1111.4325v1

Mathematics

Quantum Algebra

arXiv admin note: substantial text overlap with arXiv:1012.1956

Scientific paper

In this paper, we associate a dual quasi-bialgebra, called bosonization, to every dual quasi-bialgebra $H$ and every bialgebra $R$ in the category of Yetter-Drinfeld modules over $H$. Then, using the fundamental theorem, we characterize as bosonizations the dual quasi-bialgebras with a projection onto a dual quasi-bialgebra with a preantipode. As an application we investigate the structure of the graded coalgebra $grA$ associated to a dual quasi-bialgebra $A$ with the dual Chevalley property (e.g. $A$ is pointed).

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