2-Local derivations on the Super Virasoro algebra and Super W(2,2) algebra

Abstract

The present paper is devoted to study 2-local superderivations on the super Virasoro algebra and the super W(2, 2) algebra. We prove that all 2local superderivations on the super Virasoro algebra as well as the super W(2, 2) algebra are (global) superderivations.

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.…”

2-local derivation on the conformal Galilei algebra

“…Investigation of 2-local derivations on finite dimensional Lie algebras and infinite dimensional Lie (super) algebras were initiated in papers [3,4,6,10,12]. In [3], 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], 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 [4,6,10,12], 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.…”