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10 - Quasitriangular 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

By using categorical tools, we introduce the concept of quasitriangular (QT) quasi-bialgebras. For QT quasi-Hopf algebras we show that the square of the antipode is an inner automorphism, and therefore bijective. We uncover the QT structure of the quantum double D(H) of a finite-dimensional quasi-Hopf algebra H, and characterize D(H) as a biproduct quasi-Hopf algebra in the case when H itself is QT.

Keywords

quasitriangular quasi-Hopf algebrathe square of the antipodequantum double
Type
Chapter
Information
Quasi-Hopf Algebras
A Categorical Approach
 , pp. 381 - 406
Publisher: Cambridge University Press
Print publication year: 2019

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