On the structure of weak Hopf algebras

Details On the structure of weak Hopf algebras On the structure of weak Hopf algebras

2001-06-01

arxiv.org/abs/math/0106010v1

Mathematics

Quantum Algebra

Ams-latex, 21 page

Scientific paper

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 Tr(S^2) 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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