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Derived equivalences between generalized matrix algebras

QingHua Chen; HongJin Liu — 2020

Czechoslovak Mathematical Journal

We construct derived equivalences between generalized matrix algebras. We record several corollaries. In particular, we show that the $n$ -replicated algebras of two derived equivalent, finite-dimensional algebras are also derived equivalent.

Hall algebra of morphism category

QingHua Chen; Liwang Zhang — 2024

Czechoslovak Mathematical Journal

This paper investigates a universal PBW-basis and a minimal set of generators for the Hall algebra $ℋ (C_{2} (𝒫))$ , where $C_{2} (𝒫)$ is the category of morphisms between projective objects in a finitary hereditary exact category $𝒜$ . When $𝒜$ is the representation category of a Dynkin quiver, we develop multiplication formulas for the degenerate Hall Lie algebra $ℒ$ , which is spanned by isoclasses of indecomposable objects in $C_{2} (𝒫)$ . As applications, we demonstrate that $ℒ$ contains a Lie subalgebra isomorphic to the central extension...

Recollement of colimit categories and its applications

Ju Huang; QingHua Chen; Chunhuan Lai — 2020

Czechoslovak Mathematical Journal

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 $K$ -groups.

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Derived equivalences between generalized matrix algebras

Hall algebra of morphism category

Recollement of colimit categories and its applications