We construct derived equivalences between generalized matrix algebras. We record several corollaries. In particular, we show that the -replicated algebras of two derived equivalent, finite-dimensional algebras are also derived equivalent.
This paper investigates a universal PBW-basis and a minimal set of generators for the Hall algebra , where is the category of morphisms between projective objects in a finitary hereditary exact category . When is the representation category of a Dynkin quiver, we develop multiplication formulas for the degenerate Hall Lie algebra , which is spanned by isoclasses of indecomposable objects in . As applications, we demonstrate that contains a Lie subalgebra isomorphic to the central extension...
We give an explicit recollement for a cocomplete abelian category and its colimit category. We obtain some applications on Leavitt path algebras, derived equivalences and -groups.
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