Graded Frobenius Algebras Induced By Quivers With Twisted Superpotentials

It is proved that there is a one-to-one correspondence between twisted super-potentials and connected graded Frobenius algebras.A connected graded Frobe-nius algebra can be constructed by a twisted superpotential.In this paper we genenalize this result.We discuss graded Frobenius algebras induced by quivers We clarify twisted superpotentials can construct unconnected graded Frobenius algebras.The first chapter introduces the research background,preliminaries and also summarizes the main results of this paperIn Chapter 2,we consider a class of graded Frobenius algebras induced by quivers,and characterize the geometric properties of quivers of graded Frobenius algebras by nondegenerate biliear formsIn Chapter 3,we firstly prove that the dual coalgebra of a graded Frobe-nius algebra induced by a quiver can be generated by a single element,and then prove that this generator is a twisted superpotential.After describing the struc-ture of coalgebras generated by twisted superpotentials in details,we prove that each twisted superpotential in path coalgebras can construct a graded Frobenius algebra.Based on the above theorems and propositions,some examples are given in Chapter 4.