扭Schrodinger-Virasoro代数上Hom-李代数结构  

The Hom-Lie Algebra Structures on the Twisted Schrodinger-Virasoro Algebra

作　　者：陈秋帆 吴桐 Qiu Fan CHEN;Tong WU(Department of Mathematics,Shanghai Maritime University,Shanghai 201306,P.R.China)

机构地区：[1]上海海事大学数学系,上海201306

出　　处：《数学学报（中文版）》2023年第4期739-746,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11801363)。

摘　　要：原Schrodinger-Virasoro代数是一类重要的无限维李代数,它是在非平衡统计物理的背景下计算Schrodinger群作用共变n-点函数时引入的.扭SchrodingerVirasoro代数是原Schrodinger-Virasoro代数的扭形变.Hom-李代数是一类满足反对称和Hom-Jacobi等式的非结合代数.本文主要研究扭Schrodinger-Virasoro代数上Hom-李代数结构,确定了扭Schrodinger-Virasoro代数上存在非平凡的Hom-李代数结构.The original Schrodinger-Virasoro algebra is one kind of infinite-dimensional Lie algebra,which was originally introduced in the context of non-equilibrium statistical physics,as a by-product of the computation of n-point functions that are covariant under the action of the Schrodinger group.The twisted Schrodinger-Virasoro algebra is the twisted deformation of the original Schrodinger-Virasoro Lie algebra.Hom-Lie algebra is an anti-commutative algebra with a multiplication such that the Hom-Jacobi identity holds.In this paper,we determine all the Hom-Lie algebra structures on the twisted Schrodinger-Virasoro algebra.As a result,we get some non-trivial Hom-Lie algebra structures on the twisted Schrodinger-Virasoro algebra.

关 键 词：扭Schrodinger-Virasoro代数 Hom-李代数 自同态 

分 类 号：O152.5[理学—数学]