Local Properties Of Extended Schr?dinger-Virasoro Lie Algebra

Schr?dinger-Virasoro Lie algebra is a class of infinite dimensional Lie algebras that has important applications in mathematics and physics.It contains Schrodinger lie algebras and central-free Virasoro algebras as subalgebras.The extended Schrodinger-Virasoro Lie algebra sD is an important class of infinite dimensional Lie algebras introduced by scholars in order to study the vertex representation of Schrodinger-Virasoro Lie algebras.In the past twenty years,many scholars have extended and studied the concept of a derivation,including 2-local derivation,which is a nonlinear extension of a derivation.The 2-local derivative shows some local properties of this algebra.A map Δ from the extended Schrodinger-Virasoro Lie algebra sD into itself is called a 2-local derivation if for every x,y∈sD,there exists a derivation Dx,y of sD such that Δ(x)=Dx,y(x)and Δ(y)=Dx,y(y).In this paper,we will study 2-local derivations on extended Schrodinger-Virasoro Lie algebras.By a series of proofs we can deduce that all 2-local derivations on sD are derivations.In this paper,we will study 2-local derivations on extended Schrodinger-Virasoro Lie algebras,gradually characterize through comparison coefficients characterizing the structure of 2-Local Derivations on the extended Schrodinger-Virasoro Lie algebra sD,using Δ1=Δ-DL0,L1,Δ2=Δ1-(μχ2adM0+υχ2adN0)derived that all 2-local derivations on the extended Schrodinger-Virasoro Lie algebra sD are derivations.