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8 - Yetter–Drinfeld Module Categories

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 categories of Yetter–Drinfeld modules by computing the left and right centers of a category of modules over a quasi-bialgebra H. We then show that all four categories of Yetter–Drinfeld modules are braided isomorphic. We also introduce the quasi-Hopf algebra structure of the quantum double of a finite-dimensional quasi-Hopf algebra.

Keywords

the center of a monoidal categoryYetter-Drinfeld modulethe quantum double of a quasi-Hopf algebra
Type
Chapter
Information
Quasi-Hopf Algebras
A Categorical Approach
 , pp. 305 - 352
Publisher: Cambridge University Press
Print publication year: 2019

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