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
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 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.
