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.
作者
武亚娣
岳晓青
Ya Di WU;Xiao Qing YUE(School of Mathematical Sciences,Tongji University,Shanghai 200092,P.R.China)
出处
《数学学报（中文版）》
CSCD
北大核心
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)。
