The characteristic tilting modules of quasi-hereditary algebras which are dual extensions of directed monomial algebras are explicitly constructed; and it is shown that the Ringel dual of the dual extension of an arbi...The characteristic tilting modules of quasi-hereditary algebras which are dual extensions of directed monomial algebras are explicitly constructed; and it is shown that the Ringel dual of the dual extension of an arbitrary hereditary algebra has triangular decomposition and bipartite quiver.展开更多
For a given hereditary abelian category satisfying some finiteness conditions,in certain twisted cases it is shown that the modified Ringel-Hall algebra is isomorphic to the naive lattice algebra and there exists an e...For a given hereditary abelian category satisfying some finiteness conditions,in certain twisted cases it is shown that the modified Ringel-Hall algebra is isomorphic to the naive lattice algebra and there exists an epimorphism from the modified Ringel-Hall algebra to the lattice algebra.Furthermore,the kernel of this epimorphism is described explicitly.Finally,we show that the naive lattice algebra is invariant under the derived equivalences of hereditary abelian categories.展开更多
In the present paper we describe a specialization of prinjective Ringel-Hall algebra to 1, for prinjective modules over incidence algebras of posets of finite prinjective type, by generators and relations. This gives ...In the present paper we describe a specialization of prinjective Ringel-Hall algebra to 1, for prinjective modules over incidence algebras of posets of finite prinjective type, by generators and relations. This gives us a generalisation of Serre relations for semisimple Lie algebras. Connections of prinjective Ringel-Hall algebras with classical Lie algebras are also discussed.展开更多
In this paper, we construct the GrSbner-Shirshov bases for degenerate Ringel- Hall algebras of types A and G2 from the multiplication formulas of the corresponding generic extension monoid algebras.
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
In the present paper we investigate prinjective Ringel-Hall algebras, for prinjective modules over incidence algebras of posers of finite prinjective type. Results we obtain are analogous to these, given by C. M. Ring...In the present paper we investigate prinjective Ringel-Hall algebras, for prinjective modules over incidence algebras of posers of finite prinjective type. Results we obtain are analogous to these, given by C. M. Ringel, for representations of Dynkin quivers. In particular we give a description of prinjective Ringel-Hall algebras by generators and relations.展开更多
文摘The characteristic tilting modules of quasi-hereditary algebras which are dual extensions of directed monomial algebras are explicitly constructed; and it is shown that the Ringel dual of the dual extension of an arbitrary hereditary algebra has triangular decomposition and bipartite quiver.
基金supported by National Natural Science Foundation of China(Grant No.11701473)Youth Talent Foundation of Fuyang Normal University(Grant No.rcxm201803)。
文摘For a given hereditary abelian category satisfying some finiteness conditions,in certain twisted cases it is shown that the modified Ringel-Hall algebra is isomorphic to the naive lattice algebra and there exists an epimorphism from the modified Ringel-Hall algebra to the lattice algebra.Furthermore,the kernel of this epimorphism is described explicitly.Finally,we show that the naive lattice algebra is invariant under the derived equivalences of hereditary abelian categories.
文摘In the present paper we describe a specialization of prinjective Ringel-Hall algebra to 1, for prinjective modules over incidence algebras of posets of finite prinjective type, by generators and relations. This gives us a generalisation of Serre relations for semisimple Lie algebras. Connections of prinjective Ringel-Hall algebras with classical Lie algebras are also discussed.
文摘In this paper, we construct the GrSbner-Shirshov bases for degenerate Ringel- Hall algebras of types A and G2 from the multiplication formulas of the corresponding generic extension monoid algebras.
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.
文摘In the present paper we investigate prinjective Ringel-Hall algebras, for prinjective modules over incidence algebras of posers of finite prinjective type. Results we obtain are analogous to these, given by C. M. Ringel, for representations of Dynkin quivers. In particular we give a description of prinjective Ringel-Hall algebras by generators and relations.
