derivation2-local derivationIn this paper, we prove that every 2-local derivation on Witt algebras [Formula: see text] or [Formula: see text] is a derivation for all [Formula: see text]. As a consequence we obtain that every 2-local derivation on any centerless generalized Virasoro algebra...
A relation between 1/2-derivations of Lie algebras and transposed Poisson algebras has been established. Some non-trivial transposed Poisson algebras with a certain Lie algebra (Witt algebra, the algebra W(a, 1), the thin Lie algebra and a solvable Lie algebra with abelian nilpotent radical) ...
Let g be the Witt algebra over an infinite field of prime characteristic p. In this paper, we discuss the properties of local derivations on g, and prove that every local derivation on g is a derivation. Moreover, it is shown that there exist some local derivations which are not derivatio...
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 ...
2-Local derivations on Witt algebrasdoi:10.1142/S0219498821500687Yueqiang ZhaoYang ChenKaiming ZhaoWorld Scientific Publishing Company
As a natural generalization of derivation, 2-local derivation of a Lie algebra plays an important role in study of local properties of the Lie algebra.This paper is devoted to study 2-local derivations of Lie algebras over fields of prime characteristic. Let g be the ...