On the Lie triple derivations. Issue 21 (20th December 2022)

• Record Type: Journal Article
• Authors: Asif, Sania; Wu, Zhixiang; Munir, Mobeen
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 21(2022)
• Page Start: 6084
• Page End: 6095
• Publication Date: 2022-12-20
• Subjects: Lie triple derivation -- Jordan triple derivations -- generalized quaternion rings; Primary 11R52 -- 15A99 -- 17B67 -- 17B10 -- Secondary 16G30; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2021.1946464
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : This article aims to interpret some Lie triple derivations of Tensor algebras T ⊗ F ( a, b F ), using generalized quaternion algebra ( a, b F ) over a field F and assuming T as an F -linear associative algebra. The study concludes with complete description of all Lie triple derivations of A ⊗ F L . It is pertinent to mention here that A is assumed to be a finite-dimensional commutative algebra and L is a simple Lie algebra over an algebraically closed field.