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Free quadratic bialgebra

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Abstract

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.

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Authors and Affiliations

  1. Department of Applied Mathematics, South China University of Technology, 510641, Guangzhou, China

    Hao Zhifeng

  2. Department of Mathematics, Nanjing University, 210008, Nanjing, China

    Tong Wenting

Authors
  1. Hao Zhifeng
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  2. Tong Wenting
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Additional information

Partially supported by the National Natural Science Foundation of China.

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Zhifeng, H., Wenting, T. Free quadratic bialgebra. Acta Mathematica Sinica 12, 244–248 (1996). https://doi.org/10.1007/BF02106977

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  • DOI: https://doi.org/10.1007/BF02106977

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