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The concept of Koszul differential graded algebra (Koszul DG algebra) isintroduced. Koszul DG algebras exist extensively, and have nice propertiessimilar to the classic Koszul algebras. A DG version of the Koszul duality isproved. When the Koszul DG algebra $A$ is AS-regular, the Ext-algebra $E$ of$A$ is Frobenius. In this case, similar to the classical BGG correspondence,there is an equivalence between the stable category of finitely generated left$E$-modules, and the quotient triangulated category of the full triangulatedsubcategory of the derived category of right DG $A$-modules consisting of allcompact DG modules modulo the full triangulated subcategory consisting of allthe right DG modules with finite dimensional cohomology. The classical BGGcorrespondence can derived from the DG version.

Koszul differential graded algebras and BGG correspondence