超Heisenberg—Virasoro代数的超双导子及其应用

武亚娣, 岳晓青

数学学报 ›› 2022, Vol. 65 ›› Issue (4) : 691-698.

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数学学报 ›› 2022, Vol. 65 ›› Issue (4) : 691-698. DOI: 10.12386/A20210045
论文

超Heisenberg—Virasoro代数的超双导子及其应用

    武亚娣, 岳晓青
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Super-biderivations on the Super Heisenberg-Virasoro Algebras and Applications

    Ya Di WU, Xiao Qing YUE
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摘要

L为一个超Heisenberg-Virasoro 代数,具有一组C-基{Ln,In,Gn|nZ},满足如下关系式 [Lm,Ln]=(mn)Lm+n,[Lm,In]=nIm+n,[Lm,Gn]=nGm+n[Gm,Gn]=Im+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)I0对于所有xL 都成立, 其中f(x) 是从LC 的线性映射.

Abstract

Let L be a super Heisenberg-Virasoro algebra with the C-basis {Ln,In,Gn| nZ}, which satisfies the relations [Lm,Ln]=(mn)Lm+n, [Lm,In]=nIm+n, [Lm,Gn]=nGm+n and [Gm,Gn]=Im+n. In this paper, we prove that all super-skewsymmetric super-biderivations of L are inner. Furthermore, we prove that every linear super-commuting map on L has the form Ψ(x)=f(x)I0 for all xL, 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

Key words

super-biderivations / super-commuting maps / super Heisenberg-Virasoro algebra / Lie superalgebras

引用本文

导出引用
武亚娣, 岳晓青. 超Heisenberg—Virasoro代数的超双导子及其应用. 数学学报, 2022, 65(4): 691-698 https://doi.org/10.12386/A20210045
Ya Di WU, Xiao Qing YUE. Super-biderivations on the Super Heisenberg-Virasoro Algebras and Applications. Acta Mathematica Sinica, Chinese Series, 2022, 65(4): 691-698 https://doi.org/10.12386/A20210045

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基金

国家自然科学基金资助项目(11971350;11431010)
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