In the Ringel-Hall algebra of Dynkin type,the set of all commutator relations between the isoclasses of indecomposable representations forms a minimal Grobner-Shirshov basis and the set of the corresponding irreducibl...In the Ringel-Hall algebra of Dynkin type,the set of all commutator relations between the isoclasses of indecomposable representations forms a minimal Grobner-Shirshov basis and the set of the corresponding irreducible elements forms a PBW-type basis of the Ringel-Hall algebra.We aim to generalize this result to the reduced Drinfeld double Hall algebra of type A_(n).First,we compute a minimal Grobner-Shirshov basis for the reduced Drinfeld double Hall algebra of type An by proving that all possible compositions between the commutator relations are trivial.Then,by taking the corresponding irreducible monomials,we construct a PBW-type basis for the reduced Drinfeld double Hall algebra of type A_(n).展开更多
Let G be a group and （A, B） be a pair of multiplier Hopf algebras, where B is regular G-cograded. Let π be a crossing action of G on B, D^π=A^cop∝B=＋p∈GDπ^p with Dπ^p=A^cop∝Bp, is the Drinfeld double of the ...Let G be a group and （A, B） be a pair of multiplier Hopf algebras, where B is regular G-cograded. Let π be a crossing action of G on B, D^π=A^cop∝B=＋p∈GDπ^p with Dπ^p=A^cop∝Bp, is the Drinfeld double of the pair （A, B）, and then the deformation D^π becomes a multiplier Hopf algebra. B×A can be considered as a subalgebra of M（D^π×D^π）, the image of element b×a in B×A is （1∝b）×（a∝1） in M（D^π×D^π）. Let W =∑αWα∈ M（B×A） be a π-canonical multiplier for the pair （A, B） with Wα∈M（Bα×A） for all α∈G. The image of W in M（D^π×D^π）is a π-quasitriangular structure over D^π.展开更多
This paper is devoted to the study of the structure of the double Ringel-Hall algebra D（A） for an infinite dimensional hereditary algebra A, which is given by a valued quiver F over a finite field, and also to the ...This paper is devoted to the study of the structure of the double Ringel-Hall algebra D（A） for an infinite dimensional hereditary algebra A, which is given by a valued quiver F over a finite field, and also to the study of the relations of D（A）-modules with representations of valued quiver Г.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11861061).
文摘In the Ringel-Hall algebra of Dynkin type,the set of all commutator relations between the isoclasses of indecomposable representations forms a minimal Grobner-Shirshov basis and the set of the corresponding irreducible elements forms a PBW-type basis of the Ringel-Hall algebra.We aim to generalize this result to the reduced Drinfeld double Hall algebra of type A_(n).First,we compute a minimal Grobner-Shirshov basis for the reduced Drinfeld double Hall algebra of type An by proving that all possible compositions between the commutator relations are trivial.Then,by taking the corresponding irreducible monomials,we construct a PBW-type basis for the reduced Drinfeld double Hall algebra of type A_(n).
基金Specialized Research Fund for the Doctoral Program of Higher Education(No20060286006)the National Natural Science Foundation of China(No10871042)
文摘Let G be a group and （A, B） be a pair of multiplier Hopf algebras, where B is regular G-cograded. Let π be a crossing action of G on B, D^π=A^cop∝B=＋p∈GDπ^p with Dπ^p=A^cop∝Bp, is the Drinfeld double of the pair （A, B）, and then the deformation D^π becomes a multiplier Hopf algebra. B×A can be considered as a subalgebra of M（D^π×D^π）, the image of element b×a in B×A is （1∝b）×（a∝1） in M（D^π×D^π）. Let W =∑αWα∈ M（B×A） be a π-canonical multiplier for the pair （A, B） with Wα∈M（Bα×A） for all α∈G. The image of W in M（D^π×D^π）is a π-quasitriangular structure over D^π.
基金Project supported by the National Natural Science Foundation of China (No.10471071) the 973 Project of the Ministry of Science and Technology of China.
文摘This paper is devoted to the study of the structure of the double Ringel-Hall algebra D（A） for an infinite dimensional hereditary algebra A, which is given by a valued quiver F over a finite field, and also to the study of the relations of D（A）-modules with representations of valued quiver Г.
