Gr(?)bner-Shirshov Basis Of The Derived Hall Algebra Of Type G₂

In Ringel-Hall algebra of Dynkin type,the set S of the isomorphism classes of indecomposable modules forms a minimal Grobner-Shirshov basis of the ideal Id(S),generated by the set S,and the corresponding irreducible elements forms a PBW basis of the corresponding Ringel-Hall algbera.In this thesis,our aim is to generalize this result to the derived Hall algebra of type G₂.First,we compute the skew commutator relations among the isomorphism classes of indecomposable objects in the bounded derived category of type G₂ by using the Auslander-Reiten quiver of the bounded derived category of type G₂.Then,we prove the compositions among these skew commutator relations are trivial.Finally,we construct a PBW basis of the derived Hall algebra of type G₂.