ABSTRACT
In this paper, we study derived equivalences between triangular matrix algebras using certain classical recollements. We show that special properties of these recollements actually characterize triangular matrix algebras and describe methods to construct tilting modules and tilting complexes inducing derived equivalences between them.
Acknowledgement
The author is supported by the National Natural Science Foundation of China 11541002, the Construct Program of the Key Discipline in Hunan Province, and the Start-Up Funds of Hunan Normal University 830122-0037. He also would like to thank the anonymous referee for carefully checking the manuscript and providing many valuable suggestions to clarify a few ambiguities and improve the paper.
Notes
1Note that different from Theorem 4.5 in [Citation14], we do not need to assume that A, B, and C have finite global dimensions.
2Here generates D(Λ) if and only for for all n∈ℤ implies X = 0. But in general , which is the smallest triangulated category containing .