Notice of RetractionMaschke theorem for semilattice graded weak Hopf algebra

Notice of Retraction

After careful and considered review of the content of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE´s Publication Principles.

We hereby retract the content of this paper. Reasonable effort should be made to remove all past references to this paper.

The presenting author of this paper has the option to appeal this decision by contacting TPII@ieee.org.

In this paper, we mainly discuss the semisimplicity and the cosemisimplicity of the semilattice graded weak Hopf algebra and its relation to its direct summands, those are versions of Maschke´s theorem and dual Maschke´s theorem. Some concepts are introduced first, and we give some application about the semisimple and freeness to weak Hopf subalgebras. Finally, the results of the Maschke´s and dual Maschke´s theorem of semilattice graded weak Hopf algebra are given.