Abstract
In this paper, we obtain the following main theorem for a free quadratic bialgebraJ:
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(a)
Forp≠0,J is a pointed cosemisimple coalgebra. Forp=0,J is a hyperalgebra.
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(b)
Forp≠0 andq≠0,J has antipodeS iffp·q+2=0 andS(x)=x. Forp=0 orq=0,J has antipode andS(x)=×.
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(c)
All leftJ *-modules are rational.
Also, we give some applications in homological theory and algebraicK-theory.
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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