A_∞-algebra and Three Dimensional AS Regular Algebra

Let A be a Noetherian, connected graded algebra with global dimension 3. A is an AS regular algebra if and only if its Yoneda algebra Ext~*_A(k,k) is Frobenius algebra. Let E be a Frobenius algebra which has the same bigraded structure as Ext~*_A(k,k). First the algebra structures and the A_∞-structures of E is classified. Then applying these classifications of A_∞-structures and a corresponding relation,the “corresponding” algebras recovered from the A_∞-algebras E are obtained, which will be used for the classification of three dimensional AS regular algebras.