2-Local derivations on generalized Witt algebras

In the present paper, we study 2-local derivations on the so-called infinite dimensional generalized Witt algebras. Firstly, we prove that every 2-local derivation on the generalized Witt algebra Wn(F) over the vector space Fn is a derivation, where F is a field of characteristic zero. Further we consider generalized Witt algebras of the form W=W(G,I) over the field F, where I is an infinite index set and G=⨁i∈IZ=(ai)i∈I:ai=0 except for a finite number of i∈I, and prove that all 2-local derivations on W(G,I) are also derivations. Finally, we show that every 2-local derivation on B(Zn,I), the Borel subalgebra of Wn(F), is a derivation.