Gorenstein Properties of Simple Gluing Algebras

For given bound quiver algebras A and B, we obtain a new algebra , called the simple gluing algebra, by identifying two vertices. We investigate the Gorenstein homological property, the singularity category, the Gorenstein defect category and the Cohen-Macaulay Auslander algebra of in terms of that of A and B. Finally, we give applications to cluster-tilted algebras.