首页|PBW-Basis of Reduced Drinfeld Double Hall Algebra of Type An via Gröbner-Shirshov Basis
PBW-Basis of Reduced Drinfeld Double Hall Algebra of Type An via Gröbner-Shirshov Basis
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In the Ringel-Hall algebra of Dynkin type,the set of all commutator rela-tions between the isoclasses of indecomposable representations forms a minimal Gröbner-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 An.First,we compute a minimal Gröbner-Shirshov basis for the reduced Drinfeld double Hall algebra of type An by proving that all possible compo-sitions 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 An.
Drinfeld double Hall algebraindecomposable representationscommutator relationsGröbner-Shirshov basis
Yao Luo、Abdukadir Obul
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College of Mathematics and System Sciences,Xinjiang University Urumqi 830046,China
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