摘要
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.
