Relative D-rigid Subcategories In D-cluster Categories

Let d>1 be an integer and H be a finite dimensional hereditary algebra over an algebraically closed filed k.Let mod H be the category of finitely generated right H-modules and D^b（mod H）be the bounded dereived category with the suspension functor[1].Higher cluster categories（or d-cluster categories）are natural generalization of cluster categories which are defined as the orbit categoriesC=D^b（mod H）/τ^-1[d],whereτis the Auslander-Reiten translation on D^b（mod H）.In this thesis,we investigate the relative d-rigid subcategories based on higher cluster tilting theory.Our main results show that in a higher cluster category,the relative d-rigid subcategories with respect to a given d-rigid subcategory coincide with rigid subcategories.