Acta Mathematica Sinica

, Volume 12, Issue 3, pp 244–248 | Cite as

Free quadratic bialgebra

  • Hao Zhifeng
  • Tong Wenting


In this paper, we obtain the following main theorem for a free quadratic bialgebraJ:
  1. (a)

    Forp≠0,J is a pointed cosemisimple coalgebra. Forp=0,J is a hyperalgebra.

  2. (b)

    Forp≠0 andq≠0,J has antipodeS iffp·q+2=0 andS(x)=x. Forp=0 orq=0,J has antipode andS(x)=×.

  3. (c)

    All leftJ *-modules are rational.


Also, we give some applications in homological theory and algebraicK-theory.


Free quadratic bialgebra Antipode Cosemisimple Rational module 


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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Hao Zhifeng
    • 1
  • Tong Wenting
    • 2
  1. 1.Department of Applied MathematicsSouth China University of TechnologyGuangzhouChina
  2. 2.Department of MathematicsNanjing UniversityNanjingChina

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