Semi-derived Ringel-Hall algebras and Hall algebras of odd-periodic relative derived categories  

作　　者：Ji Lin Liangang Peng 

机构地区：[1]Department of Mathematics and Statistics,Fuyang Normal University,Fuyang 236037,China [2]School of Mathematics,Sichuan University,Chengdu 610064,China

出　　处：《Science China Mathematics》2024年第8期1735-1760,共26页中国科学（数学）（英文版）

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);University Outstanding Youth Research Project in Anhui Province(Grant No.2022AH020082);Scientific Research and Innovation Team Project of Fuyang Normal University(Grant No.TDJC2021009)。

摘　　要：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.

关 键 词：hereditary abelian categories the categories of Z/t-graded complexes semi-derived Ringel-Hall algebras derived Hall algebras 

分 类 号：O154.1[理学—数学]