Derived Equivalences of Upper Triangular Differential Graded Algebras

Details Derived Equivalences of Upper Triangular Differential Graded Algebras Derived Equivalences of Upper Triangular Differential Graded Algebras

2009-11-11

arxiv.org/abs/0911.2182v1

Mathematics

Rings and Algebras

26 pages

Scientific paper

This paper generalises a result for upper triangular matrix rings to the situation of upper triangular matrix DGA's. An upper triangular matrix DGA has the form (R,S,M) where R and S are differential graded algebras and M is a DG-left-R-right-S-bimodule. We show that under certain conditions on the DG-module M and with the existance of a DG-R-module X, from which we can build the derived category D(R), that there exists a derived equivalence between the upper triangular matrix DGAs (R,S,M) and (S,M',R'), where the DG-bimodule M' is obtained from M and X and R' is the endomorphism DGA of a K-projective resolution of X.

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