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11 - Factorizable Quasi-Hopf Algebras

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 notion of factorizable quasi-Hopf algebra by using a categorical point of view. We show that the quantum double D(H) of any finite-dimensional quasi-Hopf algebra H is factorizable, and we characterize D(H) when H itself is factorizable. Finally, we prove that any finite-dimensional factorizable quasi-Hopf algebra is unimodular. In particular, we obtain that the quantum double D(H) is a unimodular quasi-Hopf algebra.

Keywords

factorizable quasi-Hopf algebraunimodular quasi-Hopf algebra
Type
Chapter
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Quasi-Hopf Algebras
A Categorical Approach
 , pp. 407 - 450
Publisher: Cambridge University Press
Print publication year: 2019

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