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On the Structure of Weak Hopf Algebras

✍ Scribed by Dmitri Nikshych

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
252 KB
Volume
170
Category
Article
ISSN
0001-8708

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✦ Synopsis

We study the group of group-like elements of a weak Hopf algebra and derive an analogue of Radford's formula for the fourth power of the antipode S; which implies that the antipode has a finite order modulo, a trivial automorphism. We find a sufficient condition in terms of TrðS 2 Þ for a weak Hopf algebra to be semisimple, discuss relation between semisimplicity and cosemisimplicity, and apply our results to show that a dynamical twisting deformation of a semisimple Hopf algebra is cosemisimple.

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