Let Q=(Qo,Qi)be an arbitrary acyclic quiver and M an abelian category satisfying AB3 and AB3*.Let Rep(Q,M)be the category of M-valued representations of Q and Rep;(Q,M)its full subcategory consisting of representation...Let Q=(Qo,Qi)be an arbitrary acyclic quiver and M an abelian category satisfying AB3 and AB3*.Let Rep(Q,M)be the category of M-valued representations of Q and Rep;(Q,M)its full subcategory consisting of representations with 0 at vertex i.We construct a recollement of Rep(Q,M)by Rep;(Q,M)and M.If in addition,M has enough projective and injective objects,and satisfies AB4 and AB4*,then this recollement can be lifted to the derived levels.In the case that Q is finite and M is the module category Mod A over some finite dimensional algebra A,we give several direct applications concerning the relationship between homological properties of A and AQ.In particular,we find that the Cartan determinant conjecture always holds true for AQ with IQolanevennumber.展开更多
The representations of the Dynkin quivers and the corresponding Euclidean quivers are treated in many books. These notes provide three building blocks for dealing with representations of Dynkin （and Euclidean） quive...The representations of the Dynkin quivers and the corresponding Euclidean quivers are treated in many books. These notes provide three building blocks for dealing with representations of Dynkin （and Euclidean） quivers. They should be helpful as part of a direct approach to study representations of quivers, and they shed some new light on properties of Dynkin and Euclidean quivers.展开更多
As generalizations of quivers of type A,Igusa et al.introduced continuous quivers of type A.In this paper,we generalize BGP reflection functors to continuous quivers of type A,and we give another realization of the re...As generalizations of quivers of type A,Igusa et al.introduced continuous quivers of type A.In this paper,we generalize BGP reflection functors to continuous quivers of type A,and we give another realization of the reflection functor.展开更多
We describe the valued Gabriel quiver of a wedge product of coalgebras and study the category of comodules of a semiprime coalgebra. In particular, we prove that any monomial semiprime k-tame fc-tame coalgebra is stri...We describe the valued Gabriel quiver of a wedge product of coalgebras and study the category of comodules of a semiprime coalgebra. In particular, we prove that any monomial semiprime k-tame fc-tame coalgebra is string. We also prove a version of Eisenbud-Griffith theorem for coalgebras, namely, any hereditary semiprime strictly quasi-finite coalgebra is serial.展开更多
We prove that the transition matrix between a special Poincaré-Birkhoff-Witt(PBW)basis and the semicanonical basis of U+(sln(C))is upper triangular and unipotent under any order which is compatible with the parti...We prove that the transition matrix between a special Poincaré-Birkhoff-Witt(PBW)basis and the semicanonical basis of U+(sln(C))is upper triangular and unipotent under any order which is compatible with the partial order deg.展开更多
基金NSFC(Grant Nos.11701455 and 12101474)Fundamental Research Funds for the Central Universities(Grant No.2452020182).
文摘Let Q=(Qo,Qi)be an arbitrary acyclic quiver and M an abelian category satisfying AB3 and AB3*.Let Rep(Q,M)be the category of M-valued representations of Q and Rep;(Q,M)its full subcategory consisting of representations with 0 at vertex i.We construct a recollement of Rep(Q,M)by Rep;(Q,M)and M.If in addition,M has enough projective and injective objects,and satisfies AB4 and AB4*,then this recollement can be lifted to the derived levels.In the case that Q is finite and M is the module category Mod A over some finite dimensional algebra A,we give several direct applications concerning the relationship between homological properties of A and AQ.In particular,we find that the Cartan determinant conjecture always holds true for AQ with IQolanevennumber.
文摘The representations of the Dynkin quivers and the corresponding Euclidean quivers are treated in many books. These notes provide three building blocks for dealing with representations of Dynkin （and Euclidean） quivers. They should be helpful as part of a direct approach to study representations of quivers, and they shed some new light on properties of Dynkin and Euclidean quivers.
基金Supported by National Natural Science Foundation of China(No.11771445).
文摘As generalizations of quivers of type A,Igusa et al.introduced continuous quivers of type A.In this paper,we generalize BGP reflection functors to continuous quivers of type A,and we give another realization of the reflection functor.
文摘We describe the valued Gabriel quiver of a wedge product of coalgebras and study the category of comodules of a semiprime coalgebra. In particular, we prove that any monomial semiprime k-tame fc-tame coalgebra is string. We also prove a version of Eisenbud-Griffith theorem for coalgebras, namely, any hereditary semiprime strictly quasi-finite coalgebra is serial.
基金supported by National Natural Science Foundation of China (Grant Nos.11171183 and 11371165)Program for Changjiang Scholars and Innovative Research Team in University (Grant No.IRT1264)
文摘We prove that the transition matrix between a special Poincaré-Birkhoff-Witt(PBW)basis and the semicanonical basis of U+(sln(C))is upper triangular and unipotent under any order which is compatible with the partial order deg.
