Quantum commutative algebras and their duals
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If an algebraA is quantum commutative with respect to the action of a quasitriangular Hopf algebraH, then the monoidal structure on the categoryH ℳ of modules overH induces a rnonoidal structure on the categoryA#H ℳ of modules over the associated smash productA # H. The condition under which the braiding structure ofH ℳ induces a braiding structure onA#H ℳ is further investigated. Dually, the notion of quantum cocommutativity is introduced, and similar result in this dual situation is obtained.
Keywordsbraided monoidal category quantum commutative algebras quantum cocommutative coalgebras
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