We investigate the incidence algebras arising from one-branch extensions of“rectangles”.There are four different ways to form such extensions,and all four kinds of incidence algebras turn out to be derived equivalen...We investigate the incidence algebras arising from one-branch extensions of“rectangles”.There are four different ways to form such extensions,and all four kinds of incidence algebras turn out to be derived equivalent.We provide realizations for all of them as endomorphism algebra of tilting modules or tilting complexes over a Nakayama algebra.Meanwhile,an unexpected derived equivalence between Nakayama algebras N(2r-1,r)and N(2r-1,r+1)has been found.As an application,we obtain the explicit formulas of the Coxeter polynomials for a large family of Nakayama algebras,i.e.,the Nakayama algebras N(n,r)with n/2<r<n.展开更多
For any positive integer N,we clearly describe all finite-dimensional algebras A such that the upper triangular matrix algebras TN(A)are piecewise hereditary.Consequently,we describe all finite-dimensional algebras A ...For any positive integer N,we clearly describe all finite-dimensional algebras A such that the upper triangular matrix algebras TN(A)are piecewise hereditary.Consequently,we describe all finite-dimensional algebras A such that their derived categories of N-complexes are triangulated equivalent to derived categories of hereditary abelian categories,and we describe the tensor algebras A⊗K[X]/(X^(N))for which their singularity categories are triangulated orbit categories of the derived categories of hereditary abelian categories.展开更多
基金Supported by the Natural Science Foundation of Xiamen(Grant No.3502Z20227184)the Natural Science Foundation of Fujian Province(Grant No.2022J01034)+2 种基金the Natural Science Foundation of Shanghai(Grant No.23ZR1435100)the National Natural Science Foundation of China(Grant Nos.12271448 and 12301054)the Fundamental Research Funds for Central Universities of China(Grant No.20720220043)。
文摘We investigate the incidence algebras arising from one-branch extensions of“rectangles”.There are four different ways to form such extensions,and all four kinds of incidence algebras turn out to be derived equivalent.We provide realizations for all of them as endomorphism algebra of tilting modules or tilting complexes over a Nakayama algebra.Meanwhile,an unexpected derived equivalence between Nakayama algebras N(2r-1,r)and N(2r-1,r+1)has been found.As an application,we obtain the explicit formulas of the Coxeter polynomials for a large family of Nakayama algebras,i.e.,the Nakayama algebras N(n,r)with n/2<r<n.
文摘For any positive integer N,we clearly describe all finite-dimensional algebras A such that the upper triangular matrix algebras TN(A)are piecewise hereditary.Consequently,we describe all finite-dimensional algebras A such that their derived categories of N-complexes are triangulated equivalent to derived categories of hereditary abelian categories,and we describe the tensor algebras A⊗K[X]/(X^(N))for which their singularity categories are triangulated orbit categories of the derived categories of hereditary abelian categories.
