论文标题
在山地上弱的HOPF代数的部分共同体
Partial Coactions of Weak Hopf Algebras on Coalgebras
论文作者
论文摘要
可以看出，如果$ h $是薄弱的霍普夫代数，那么在煤层\ cite {wang}上的弱双子骨的共同行动的定义中，则抑制了定义属性，从而导致了（全球）型霍普夫代数对煤层的（全球）共同。下一步将是通过弱霍普夫代数上的固定元素引入弱霍夫代数的部分共同体以及一个示例家庭的局部概念，这两个定义都说明了：全球和部分。此外，还将介绍如何通过投影从全球占地界局部获得部分综合山地，从而提供另一种方法来查找弱霍普夫代数局部局部共同体的示例。此外，将研究弱的粉碎coproduct \ cite {wang}，在哪种条件下，可以从coproduct以及在其上定义的cousit产生弱的Hopf代数结构。最后，将建立部分作用的结构与弱霍普夫代数在山地上的部分共同关系之间的双重关系。
It will be seen that if $H$ is a weak Hopf algebra in the definition of coaction of weak bialgebras on coalgebras \cite{Wang}, then a definition property is suppressed giving rise to the (global) coactions of weak Hopf algebras on coalgebras. The next step will be introduce the more general notion of partial coactions of weak Hopf algebras on coalgebras as well as a family of examples via a fixed element on the weak Hopf algebra, illustrating both definitions: global and partial. Moreover, it will also be presented how to obtain a partial comodule coalgebra from a global one via projections, giving another way to find examples of partial coactions of weak Hopf algebras on coalgebras. In addition, the weak smash coproduct \cite{Wang} will be studied and it will be seen under what conditions it is possible to generate a weak Hopf algebra structure from the coproduct and the counit defined on it. Finally, a dual relationship between the structures of partial action and partial coaction of a weak Hopf algebra on a coalgebra will be established.
