In this paper,we introduce the theory of local cohomology and local duality to Notherian connected cochain DG algebras.We show that the notion of the local cohomology functor can be used to detect the Gorensteinness o...In this paper,we introduce the theory of local cohomology and local duality to Notherian connected cochain DG algebras.We show that the notion of the local cohomology functor can be used to detect the Gorensteinness of a homologically smooth DG algebra.For any Gorenstein homologically smooth locally finite DG algebra A,we define a group homomorphism Hdet:Aut_(dg)(A)→k^(×),called the homological determinant.As applications,we present a sufficient condition for the invariant DG subalgebra A^(G)to be Gorenstein,where A is a homologically smooth DG algebra such that H(A)is a Noetherian AS-Gorenstein graded algebra and G is a finite subgroup of Aut_(dg)(A).Especially,we can apply this result to DG down-up algebras and non-trivial DG free algebras generated in two degree-one elements.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11871326)。
文摘In this paper,we introduce the theory of local cohomology and local duality to Notherian connected cochain DG algebras.We show that the notion of the local cohomology functor can be used to detect the Gorensteinness of a homologically smooth DG algebra.For any Gorenstein homologically smooth locally finite DG algebra A,we define a group homomorphism Hdet:Aut_(dg)(A)→k^(×),called the homological determinant.As applications,we present a sufficient condition for the invariant DG subalgebra A^(G)to be Gorenstein,where A is a homologically smooth DG algebra such that H(A)is a Noetherian AS-Gorenstein graded algebra and G is a finite subgroup of Aut_(dg)(A).Especially,we can apply this result to DG down-up algebras and non-trivial DG free algebras generated in two degree-one elements.
