2-Local derivations on generalized Witt algebras. Issue 16 (10th December 2021) - Ayupov, Shavkat; Kudaybergenov, Karimbergen; Yusupov, Baxtiyor
Abstract : 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 W n ( F ) over the vector space F n 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 ∈ I Z = ( a i ) i ∈ I : a i = 0   e x c e p t   f o r   a   f i n i t e   n u m b e r   o f   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 ( Z n, I ), the Borel subalgebra of W n ( F ), is a derivation.