正分次代数上的一些同调性质

Some Homological Properties of Positive Graded Algebras

将前人关于连通分次代数的一些结论推广到零阶部分为Artin半单环的正分次代数上.主要讨论了一般正分次代数为Gorenstein代数与它的平凡模Ext代数为Frobenius代数的关系,并得到结论:若A是整体维数有限的Koszul代数,且A是左有限的,则A是左Gorenstein代数当且仅当它的Koszul对偶A!是右Frobenius代数.

Some homological properties of connected graded algebras are generalized to more general graded algebras.A general definition of (graded) Frobenius algebra is given on graded algebra,and a criteria to decide when an algebra is a Frobenius algebra is given.The relation between the Frobenius algebras and Gorenstein algebras for the general case are studied.One of the main results is:Let A be a Koszul algebra of finite global dimension with A_0=kk...k at its zero position and A is left finite,then A is left Gorenstein if and only if A~! is righ Frobenius.