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The paper is concerned with the semisimplicity of smash products of generalized quantum commutative algebras in weak Hopf algebra setting. Let H be a weak Hopf algebra over a field k andA any semisimple and generalized quantum commutative weak Yetter-Drinfeld H -module algebra. It is shown that A]H is semisimple if and only if A is a projective left A]H module. Applying results to quasitriangular (weak) Hopf algebras is considered. 2010 Mathematics Subject Classification: 16W30

The Maschke-type theorem of smash products of generalized quantum commutative algebras over weak Hopf algebras