A_∞-代数与三维AS正则代数

A_∞-algebra and Three Dimensional AS Regular Algebra

利用A∞ 代数来讨论Artin Schelter(AS)正则代数的分类 .设A是整体维数为 3的连通分次Noetherian代数 ,则A是AS正则代数当且仅当它的Yoneda代数Ext A(k ,k)是Frobenius代数 .设E是与Ext A(k ,k)有相同的双分次结构的Frobenius代数 .首先对E的代数结构及A∞ 结构作分类 ,然后利用这个A∞ 结构的分类及已知的一个对应关系 ,得到A∞ 代数E的“对应”代数 ,从而为三维AS正则代数的A∞

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.