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Quantum commutative algebras and their duals

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Hunan Normal University, 410081, Changsha, China

    Guoquan Hu

  2. Institute of Mathematics, Fudan University, 200433, Shanghai, China

    Yonghua Xu

Authors
  1. Guoquan Hu
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  2. Yonghua Xu
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Hu, G., Xu, Y. Quantum commutative algebras and their duals. Sci. China Ser. A-Math. 40, 243–252 (1997). https://doi.org/10.1007/BF02874516

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  • DOI: https://doi.org/10.1007/BF02874516

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