The semisimplicity of smash products of quantum commutative algebras

Abstract

Let H be a finite dimensional quasitriangular Hopf algebra over a field k and A a quantum commutative H-module algbera. It is shown that if A is semisimple, then A:#H is semisimple if and only if t.c = 1 for some c ∊ A where .

Keywords:

• quasitriangular Hopf algbera
• semisimple algebra
• Maschke’s theorem

1991 Mathematics Subject Classification:

• 16S40
• 16W30