Science in China Series A: Mathematics

, Volume 40, Issue 3, pp 243–252 | Cite as

Quantum commutative algebras and their duals

  • Guoquan Hu
  • Yonghua Xu


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


braided monoidal category quantum commutative algebras quantum cocommutative coalgebras 


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Copyright information

© Science in China Press 1997

Authors and Affiliations

  • Guoquan Hu
    • 1
  • Yonghua Xu
    • 2
  1. 1.Department of MathematicsHunan Normal UniversityChangshaChina
  2. 2.Institute of MathematicsFudan UniversityShanghaiChina

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