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9 - Two-sided Two-cosided Hopf Modules

Published online by Cambridge University Press:  21 February 2019

Daniel Bulacu ,
Stefaan Caenepeel ,
Florin Panaite  and
Freddy Van Oystaeyen
Daniel Bulacu
Affiliation:
Universitatea din Bucureşti, Romania
Stefaan Caenepeel
Affiliation:
Vrije Universiteit Brussel
Florin Panaite
Affiliation:
Institute of Mathematics of the Romanian Academy
Freddy Van Oystaeyen
Affiliation:
Universiteit Antwerpen, Belgium
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Summary

We introduce the category of two-sided two-cosided Hopf modules over a quasi-bialgebra H and show that it is braided monoidally equivalent to the category of Yetter–Drinfeld modules over H, provided that H is a quasi-Hopf algebra. We use this equivalence to obtain structure theorems for bicomodule algebras and bimodule coalgebras over H. Finally, we show that a Hopf algebra within this braided monoidal category identifies with a quasi-Hopf algebra with projection.

Keywords

two-sided two-cosided Hopf modulebicomodule algebrabimodule coalgebraquasi-Hopf algebra with projection
Type
Chapter
Information
Quasi-Hopf Algebras
A Categorical Approach
 , pp. 353 - 380
Publisher: Cambridge University Press
Print publication year: 2019

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