In this paper, we obtain the following main theorem for a free quadratic bialgebra J: (a) For p≠0, J is a pointed cosemisimple coalgebra. For p=0, J is a hyperalgebra. (b) For p≠0 and q≠0, J has antipode S iff p...In this paper, we obtain the following main theorem for a free quadratic bialgebra J: (a) For p≠0, J is a pointed cosemisimple coalgebra. For p=0, J is a hyperalgebra. (b) For p≠0 and q≠0, J has antipode S iff p·q+2=0 and S(x)=x. Forp=0 or q=0, J has antipode and S(x)=-x. (c) All left J*-modules are rational. Also, we give some applications in homological theory and algebraic K-theory.展开更多
基金Partially supported by the National Natural Science Foundation of China.
文摘In this paper, we obtain the following main theorem for a free quadratic bialgebra J: (a) For p≠0, J is a pointed cosemisimple coalgebra. For p=0, J is a hyperalgebra. (b) For p≠0 and q≠0, J has antipode S iff p·q+2=0 and S(x)=x. Forp=0 or q=0, J has antipode and S(x)=-x. (c) All left J*-modules are rational. Also, we give some applications in homological theory and algebraic K-theory.
