设H是一个双代数,B是带有H弱作用的代数,σ:H(?)H→B和τ:H(?)H→B都是k-双线性映射.首先我们给出了B_χ^(#_σ^τ)H成为双代数的充分必要条件,此双代数带有扭曲交叉积B#_σ~τH和冲余积B×H,其中B是H上的余模余代数.此双代数是由Ra...设H是一个双代数,B是带有H弱作用的代数,σ:H(?)H→B和τ:H(?)H→B都是k-双线性映射.首先我们给出了B_χ^(#_σ^τ)H成为双代数的充分必要条件,此双代数带有扭曲交叉积B#_σ~τH和冲余积B×H,其中B是H上的余模余代数.此双代数是由Radford首次在文献[8]中提出,后来Doi and Takeuchi又在文献[4]和[9]中进一步推广而得到的.然后我们对此双代数进行刻画并研究其基本性质.最后我们给出了此双代数成为Hopf代数的充分条件.展开更多
First, we present semisimple properties of twisted products by means of constructing an algebra isomorphism between twisted products and crossed products, and point out that there exist some relations among braided bi...First, we present semisimple properties of twisted products by means of constructing an algebra isomorphism between twisted products and crossed products, and point out that there exist some relations among braided bialgebras, paired bialgebras and Yang-Baxter coalgebras. Furthermore, we give an example to illustrate these relations by using Sweedler's 4-dimensional Hopf algebra. Finally, from starting off with Yang-Baxter coalgebras, we can construct some quadratic bialgebras such that they are braided bialgebras.展开更多
基金Supported by the FNS of China(10871042)the SRFDPHE(20060286006)the EMSTRKF of China(108154).
文摘设H是一个双代数,B是带有H弱作用的代数,σ:H(?)H→B和τ:H(?)H→B都是k-双线性映射.首先我们给出了B_χ^(#_σ^τ)H成为双代数的充分必要条件,此双代数带有扭曲交叉积B#_σ~τH和冲余积B×H,其中B是H上的余模余代数.此双代数是由Radford首次在文献[8]中提出,后来Doi and Takeuchi又在文献[4]和[9]中进一步推广而得到的.然后我们对此双代数进行刻画并研究其基本性质.最后我们给出了此双代数成为Hopf代数的充分条件.
文摘First, we present semisimple properties of twisted products by means of constructing an algebra isomorphism between twisted products and crossed products, and point out that there exist some relations among braided bialgebras, paired bialgebras and Yang-Baxter coalgebras. Furthermore, we give an example to illustrate these relations by using Sweedler's 4-dimensional Hopf algebra. Finally, from starting off with Yang-Baxter coalgebras, we can construct some quadratic bialgebras such that they are braided bialgebras.
