Let A be an arbitrary hereditary abelian category. Lu and Peng (2021) defined the semi-derived Ringel-Hall algebra SDH(A) of A and proved that SDH(A) has a natural basis and is isomorphic to the Drinfeld double Ringel...Let A be an arbitrary hereditary abelian category. Lu and Peng (2021) defined the semi-derived Ringel-Hall algebra SDH(A) of A and proved that SDH(A) has a natural basis and is isomorphic to the Drinfeld double Ringel-Hall algebra of A. In this paper, we introduce a coproduct formula on SDH(A) with respect to the basis of SDH(A) and prove that this coproduct is compatible with the product of SDH(A), and thereby the semi-derived Ringel-Hall algebra of A is endowed with a bialgebra structure which is identified with the bialgebra structure of the Drinfeld double Ringel-Hall algebra of A.展开更多
The main result of this paper is that any two non-isomorphic indecomposable modules of a cluster-tilted algebra of finite representation type have different dimension vectors. As an application to cluster algebras of ...The main result of this paper is that any two non-isomorphic indecomposable modules of a cluster-tilted algebra of finite representation type have different dimension vectors. As an application to cluster algebras of Types A, D, E, we give a proof of the Fomin Zelevinsky denominators conjecture for cluster variables, namely, different cluster variables have different denominators with respect to any given cluster.展开更多
Let t be a positive integer and A be a hereditary abelian category satisfying some finiteness conditions.We define the semi-derived Ringel-Hall algebra of A from the category C_(Z/t)(A)of Z/t-graded complexes and obta...Let t be a positive integer and A be a hereditary abelian category satisfying some finiteness conditions.We define the semi-derived Ringel-Hall algebra of A from the category C_(Z/t)(A)of Z/t-graded complexes and obtain a natural basis of the semi-derived Ringel-Hall algebra.Moreover,we describe the semiderived Ringel-Hall algebra by the generators and defining relations.In particular,if t is an odd integer,we show an embedding of the derived Hall algebra of the odd-periodic relative derived category in the extended semi-derived Ringel-Hall algebra.展开更多
文摘Let A be an arbitrary hereditary abelian category. Lu and Peng (2021) defined the semi-derived Ringel-Hall algebra SDH(A) of A and proved that SDH(A) has a natural basis and is isomorphic to the Drinfeld double Ringel-Hall algebra of A. In this paper, we introduce a coproduct formula on SDH(A) with respect to the basis of SDH(A) and prove that this coproduct is compatible with the product of SDH(A), and thereby the semi-derived Ringel-Hall algebra of A is endowed with a bialgebra structure which is identified with the bialgebra structure of the Drinfeld double Ringel-Hall algebra of A.
基金Supported partially by the National 973 Programs (Grant No. 2006CB805905)
文摘The main result of this paper is that any two non-isomorphic indecomposable modules of a cluster-tilted algebra of finite representation type have different dimension vectors. As an application to cluster algebras of Types A, D, E, we give a proof of the Fomin Zelevinsky denominators conjecture for cluster variables, namely, different cluster variables have different denominators with respect to any given cluster.
基金supported by National Natural Science Foundation of China(Grant Nos.12001107 and 11821001)University Natural Science Project of Anhui Province(Grant No.KJ2021A0661)+1 种基金University Outstanding Youth Research Project in Anhui Province(Grant No.2022AH020082)Scientific Research and Innovation Team Project of Fuyang Normal University(Grant No.TDJC2021009)。
文摘Let t be a positive integer and A be a hereditary abelian category satisfying some finiteness conditions.We define the semi-derived Ringel-Hall algebra of A from the category C_(Z/t)(A)of Z/t-graded complexes and obtain a natural basis of the semi-derived Ringel-Hall algebra.Moreover,we describe the semiderived Ringel-Hall algebra by the generators and defining relations.In particular,if t is an odd integer,we show an embedding of the derived Hall algebra of the odd-periodic relative derived category in the extended semi-derived Ringel-Hall algebra.
