The concept of Koszul differential graded (DG for short) algebra is introduced in [8].Let A be a Koszul DG algebra.If the Ext-algebra of A is finite-dimensional,i.e.,the trivial module A k is a compact object in the d...The concept of Koszul differential graded (DG for short) algebra is introduced in [8].Let A be a Koszul DG algebra.If the Ext-algebra of A is finite-dimensional,i.e.,the trivial module A k is a compact object in the derived category of DG A-modules,then it is shown in [8] that A has many nice properties.However,if the Ext-algebra is infinitedimensional,little is known about A.As shown in [15] (see also Proposition 2.2),A k is not compact if H(A) is finite-dimensional.In this paper,it is proved that the Koszul duality theorem also holds when H(A) is finite-dimensional by using Foxby duality.A DG version of the BGG correspondence is deduced from the Koszul duality theorem.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 10801099,10731070)the Doctoral Program Foundation of the Ministry of Education of China (No. 20060246003)
文摘The concept of Koszul differential graded (DG for short) algebra is introduced in [8].Let A be a Koszul DG algebra.If the Ext-algebra of A is finite-dimensional,i.e.,the trivial module A k is a compact object in the derived category of DG A-modules,then it is shown in [8] that A has many nice properties.However,if the Ext-algebra is infinitedimensional,little is known about A.As shown in [15] (see also Proposition 2.2),A k is not compact if H(A) is finite-dimensional.In this paper,it is proved that the Koszul duality theorem also holds when H(A) is finite-dimensional by using Foxby duality.A DG version of the BGG correspondence is deduced from the Koszul duality theorem.
