Some applications of recollements to Gorenstein projective modules

Ming Lu

Published 2014-12-02Version 1

We apply the technique of recollement to study the Gorenstein projective modules. First, we construct a recollement of defect Gorenstein categories for the upper triangular matrix algebras. Then we use the defect Gorenstein category to give a categorical interpretation of the Groenstein properties of the upper triangular matrix algebra obtained by X-W Chen, B. Xiong and P. Zhang respectively. Finally, as a generalization of the structure of the cluster-tilted algebra of type $A$, we define the gluing Nakayama algebra, and use recollement to describe its singularity category clearly.