MMN-1021
The Maschke-type theorem of smash products of generalized quantum commutative algebras over weak Hopf algebras
Abstract
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 $k$ and $A$ any semisimple and generalized quantum commutative weak Yetter-Drinfeld $H$-module
algebra. It is shown that $A \sharp H$ is semisimple if and only if $A$ is a projective left $A \sharp H$-module. Applying results to quasitriangular (weak) Hopf algebras is considered.
Vol. 16 (2015), No. 1, pp. 91-99
DOI: 10.18514/MMN.2015.1021