Article

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

, Volume 81, Issue 1, pp 35-44

First online:

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

  • Wen-juan ZhaiAffiliated withDepartment of Mathematics, Nanjing Agricultural University
  • , Liang-yun ZhangAffiliated withDepartment of Mathematics, Nanjing Agricultural University Email author 

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Abstract

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).

Keywords

Quasitriangular weak Hopf algebra Weak module algebra Weak smash product Maschke’s theorem

Mathematics Subject Classification (2000)

16W30