Centroid Hom-associative Algebras and Centroid Hom-Lie Algebras  

作　　者：Yu Xiu BAI Leonid A.BOKUT Yu Qun CHEN Ze Rui ZHANG 

机构地区：[1]Department of Mathematics Teaching,Guangzhou Civil Aviation College,Guangzhou 510403,P.R.China [2]Sobolev Institute of Mathematics,Novosibirsk 630090,Russia [3]Novosibirsk State University,Novosibirsk 630090,Russia [4]School of Mathematical Sciences,South China Normal University,Guangzhou 510631,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第4期935-961,共27页数学学报（英文版）

基　　金：the grant of Guangzhou Civil Aviation College(Grant No.22X0430);the RAS Fundamental Research Program(Grant No.FWNF-2022-0002);the NNSF of China(Grant Nos.11571121,12071156);the NNSF of China(Grant No.12101248);the China Postdoctoral Science Foundation(Grant No.2021M691099)。

摘　　要：In this article,we construct free centroid hom-associative algebras and free centroid hom-Lie algebras.We also construct some other relatively free centroid hom-associative algebras by applying the Gr?bner-Shirshov basis theory for(unital)centroid hom-associative algebras.Finally,we prove that the"Poincaré-Birkhoff-Witt theorem"holds for certain type of centroid hom-Lie algebras over a field of characteristic 0,namely,every centroid hom-Lie algebra such that the eigenvectors of the mapβlinearly generates the whole algebra can be embedded into its universal enveloping centroid hom-associative algebra,and the linear basis of the universal enveloping algebra does not depend on the multiplication table of the centroid hom-Lie algebra under consideration.

关 键 词：Centroid hom-Lie algebra centroid hom-associative algebra Gr?bner-Shirshov basis 

分 类 号：O152.5[理学—数学]