Maschke’s theorem for smash products of quasitriangular weak Hopf algebras


DOI: 10.1007/s12188-010-0047-7

Cite this article as:
Zhai, W. & Zhang, L. Abh. Math. Semin. Univ. Hambg. (2011) 81: 35. doi:10.1007/s12188-010-0047-7


The paper is concerned with the semisimplicity of smash products of quasitriangular weak Hopf algebras. Let (H,R) be a finite dimensional quasitriangular weak Hopf algebra over a field k and A any semisimple and quantum commutative weak H-module algebra. Based on the work of Nikshych et al. (Topol. Appl. 127(1–2):91–123, 2003), we give Maschke’s theorem for smash products of quasitriangular weak Hopf algebras, stating that A#H is semisimple if and only if A is a projective left A#H-module, which extends the Theorem 3.2 given in Yang and Wang (Commun. Algebra 27(3):1165–1170, 1999).


Quasitriangular weak Hopf algebraWeak module algebraWeak smash productMaschke’s theorem

Mathematics Subject Classification (2000)


Copyright information

© Mathematisches Seminar der Universität Hamburg and Springer 2011

Authors and Affiliations

  1. 1.Department of MathematicsNanjing Agricultural UniversityNanjingP.R. China