2-Local derivations on Witt algebras

Abstract

In this paper, we prove that every 2-local derivation on Witt algebras W n , W + n or W ++ n is a derivation for all n = 1, 2, · · · , ∞.

2-local derivations on the Jacobson-Witt algebras in prime characteristic

“…Similar results on 2-local derivations on simple Leibniz algebras were obtained in [1]. All 2-local derivation on Witt algebras and some of their subalgebras were shown to be derivations in [16,3]. Similar result was obtained quite recently for the Walgebra W (2, 2) in [14].…”

Local and $2$-local automorphisms of simple generalized Witt algebras

“…For local automorphisms of Lie algebras it was only known that the automorphisms and the anti-automorphisms of finite dimensional simple Lie algebra exhaust all its local automorphisms in [8]. For infinite dimensional Lie algebras, 2-local derivations on Witt algebras were determined using different approaches in [2] and [16]. We determined all local derivations on Witt algebras in [7].…”

2-local derivations on the twisted Heisenberg-Virasoro algebra

“…Investigation of 2-local derivations on finite dimensional Lie algebras and infinite dimensional Lie (super) algebras were initiated in papers [2,3,4,10,11]. In [2], the authors proved that every 2-local derivation on a semi-simple Lie algebra is a derivation and that each finite-dimensional nilpotent Lie algebra with dimension larger than two admits 2-local derivation which is not a derivation.…”

“…In [2], the authors proved that every 2-local derivation on a semi-simple Lie algebra is a derivation and that each finite-dimensional nilpotent Lie algebra with dimension larger than two admits 2-local derivation which is not a derivation. In [3,4,10,11], the authors proved that 2-local derivations on the Witt algebra, super Virasoro algebra, W-algebra W (2, 2) and its superalgebra are derivations and there are 2-local derivations on the so-called thin Lie algebra which are not derivations.…”