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Keywords:
(strongly) Gorenstein injective module; upper triangular matrix Artin algebra; triangulated category; recollement
(strongly) Gorenstein injective module; upper triangular matrix Artin algebra; triangulated category; recollement
Summary:
Let $\Lambda =\left (\begin {smallmatrix} A&M\\ 0&B \end {smallmatrix}\right )$ be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective $\Lambda $-modules under the condition that $M$ is a cocompatible $(A,B)$-bimodule, we establish a recollement of the stable category $\overline {\rm Ginj(\Lambda )}$. We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over $\Lambda $.
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