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12 - The Quantum Dimension and Involutory 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 compute the quantum dimension of a finite-dimensional quasi-Hopf algebra H and of its quantum double D(H), within the rigid braided category of finite-dimensional left D(H)-modules. This involves the semisimplicity of D(H) and leads to the notion of involutory quasi-Hopf algebra, studied at the end of the chapter.

Keywords

quantum dimensioninvolutory quasi-Hopf algebrasemisimple quantum double
Type
Chapter
Information
Quasi-Hopf Algebras
A Categorical Approach
 , pp. 451 - 480
Publisher: Cambridge University Press
Print publication year: 2019

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