| This thesis mainly deals with pointed coalgebras. Our idealsand methods come from the representation theory of finite dimen-sional algebras, especially the quiver-theoretic method. It consistsof the following two parts.Starting with a discussion of the coradical filtration of pointedcoalgebras in the second chapter,we give a vector space comple-ment of Cn?1 in Cn and generalize the Taft-Wilson Theorem.In the third chapter, we study a special pointed coalgebras-path coalgebras. For any given quiver Q, we proof the equivalenceof MkQc and the locally nilpotent subcategory of Repk(Q), andwe obtain a characterization of the category of finite dimensionalrepresentations on basic cycles over algebraically closed field. |
