2-Local derivations on generalized Witt algebras. Issue 16 (10th December 2021)

• Record Type: Journal Article
• Authors: Ayupov, Shavkat; Kudaybergenov, Karimbergen; Yusupov, Baxtiyor
• Is Part Of: Linear & multilinear algebra. Volume 69:Issue 16(2021)
• Page Start: 3130
• Page End: 3140
• Publication Date: 2021-12-10
• Subjects: Generalized Witt algebra -- derivation -- 2-local derivation; 16W25 -- 16W10 -- 17B20 -- 17B40; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2019.1708846
• Languages: English
• ISSNs: 0308-1087

Abstract

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.