PBW-Basis of Reduced Drinfeld Double Hall Algebra of Type An via Grobner-Shirshov Basis  

作　　者：Yao Luo Abdukadir Obul 

机构地区：[1]College of Mathematics and System Sciences,Xinjiang University Urumqi 830046,China

出　　处：《Algebra Colloquium》2023年第1期43-60,共18页代数集刊（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11861061).

摘　　要：In the Ringel-Hall algebra of Dynkin type,the set of all commutator relations between the isoclasses of indecomposable representations forms a minimal Grobner-Shirshov basis and the set of the corresponding irreducible elements forms a PBW-type basis of the Ringel-Hall algebra.We aim to generalize this result to the reduced Drinfeld double Hall algebra of type A_(n).First,we compute a minimal Grobner-Shirshov basis for the reduced Drinfeld double Hall algebra of type An by proving that all possible compositions between the commutator relations are trivial.Then,by taking the corresponding irreducible monomials,we construct a PBW-type basis for the reduced Drinfeld double Hall algebra of type A_(n).

关 键 词：Drinfeld double Hall algebra indecomposable representations commutator relations Grobner-Shirshov basis 

分 类 号：O15[理学—数学]