超Heisenberg-Virasoro代数的超双导子及其应用  

Super-biderivations on the super Heisenberg-Virasoro algebras and applications

作　　者：武亚娣 岳晓青[1] Ya Di WU;Xiao Qing YUE(School of Mathematical Sciences,Tongji University,Shanghai 200092,P.R.China)

机构地区：[1]同济大学数学科学学院,上海200092

出　　处：《数学学报（中文版）》2022年第4期691-698,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11971350,11431010)。

摘　　要：令L为一个超Heisenberg-Virasoro代数,具有一组C-基:{L_(n),I_(n),G_(n)|n∈Z},满足如下关系式:[L_(m),L_(n)]=(m-n)L_(m)+n,[L_(m),I_(n)]=-nI_(m+n),[L_(m),G_(n)]=-nG_(m+n)和[Gm,G_(n)]=I_(m+n).本文证明了L的所有超反对称超双导子都是内导子.进一步,我们还证明了L上的每个线性超交换映射都具有这样的形式:Ψ(x)=f(x)I_(0)对于所有x∈L都成立,其中f(x)是从L到C的线性映射.Let L be a super Heisenberg-Virasoro algebra with the C-basis{L_(n),I_(n),G_(n)|n∈Z},which satisfies the relations[L_(m),L_(n)]=(m-n)L_(m)+n,[L_(m),I_(n)]=-nI_(m+n),[L_(m),G_(n)]=-nG_(m+n)and[G_(m),G_(n)]=I_(m+n).I_(n)this paper,we prove that all superskewsymmetric super-biderivations of L are inner.Furthermore,we prove that every linear super-commuting map on L has the formΨ(x)=f(x)I_(0)for all x∈L,where f(x)is a linear map from L to C.

关 键 词：超双导子 超交换映射 超Heisenberg-Virasoro代数 李超代数 

分 类 号：G633.62[文化科学—教育学]