Products of Commutator Ideals of Some Lie-admissible Algebras  

作　　者：Ivan KAYGORODOV Farukh MASHUROV Tran Giang NAM Ze Rui ZHANG 

机构地区：[1]CMA-UBI,Universidade da Beira Interior,Covilha,Portugal [2]Shenzhen International Center for Mathematics(SICM),Southern University of Science and Technology,Shenzhen 518055,P.R.China [3]Institute of Mathematics,VAST,18 Hoang Quoc Viet,Cau Giay,Hanoi,Vietnam [4]School of Mathematical Sciences,South China Normal University,Guangzhou 510631,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第8期1875-1892,共18页数学学报（英文版）

基　　金：supported by FCT(Grant No.UIDB/00212/2020);FCT(Grant No.UIDP/00212/2020);supported by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan(Grant No.AP14869221);by“Tayelsizdik urpaqtary”MISD RK;partially supported by the Simons Foundation Targeted Grant for the Institute of Mathematics–VAST(Grant No.558672);by the Vietnam Institute for Advanced Study in Mathematics(VIASM);supported by the NNSF of China(Grant No.12101248);by the China Postdoctoral Science Foundation(Grant No.2021M691099)。

摘　　要：In this article,we mainly study the products of commutator ideals of Lie-admissible algebras such as Novikov algebras,bicommutative algebras,and assosymmetric algebras.More precisely,we first study the properties of the lower central chains for Novikov algebras and bicommutative algebras.Then we show that for every Lie nilpotent Novikov algebra or Lie nilpotent bicommutative algebra A,the ideal of A generated by the set{ab−ba|a,b∈A}is nilpotent.Finally,we study properties of the lower central chains for assosymmetric algebras,study the products of commutator ideals of assosymmetric algebras and show that the products of commutator ideals have a similar property as that for associative algebras.

关 键 词：Novikov algebra bicommutative algebra assosymmetric algebra Lie nilpotent algebra 

分 类 号：O15[理学—数学]