The Structures Of Weak Hopf Algebras Corresponding To Taft Algebra

The article extends the research methods and research results of the structure of weak quantum groups corresponding to Sweedler algebra to the the structures of weak Hopf algebras corresponding to Taft algebras. Then, this article studies the algebra and coalgebra of the structures of weak Hopf algebras corresponding to Taft algebras. However, Sweedler algebra is compared with Taft algebra that the Taft algebra is the extention of the Sweedler algebra. So, the structures of weak Hopf algebras corresponding to Taft algebras have more complex structures; Therefore, this article selectes the weak Hopf algebras corresponding to Taft algebra for the study object; Further, The algebra structure and coalgebra structure are studied by the structures of weak Hopf algebras corresponding to Taft algebras. So, this article can be divided into the following sections.Firstly, this article uses the case the multiplication and the comultiplication combinations of generators, tectonic weak Hopf algebra method is obtained, and then get more examples of weak Hopf algebras, which have been calculated that there are three constitute the weak Hopf algebras corresponding to Taft algebras, so that there are three structures of weak Hopf algebras corresponding to Taft algebras.Secondly, this article describes the algebra structures of weak Hopf algebras corresponding to Taft algebras, that is the weak Hopf algebras corresponding to Taft algebras are decomposed into a direct sum of two algebras, one of which is Taft algebra;Finally, this article describes the coalgebra structures of weak Hopf algebras corresponding to Taft algebras, that is the coalgebra structures of these weak Hopf algebras described by their Ext quivers, the weak Hopf algebras corresponding to Taft algebra has a sub-Hopf algebra which is isomorphic to Taft algebra.