Characterizations of Lie derivations of triangular algebras

✍ Scribed by Peisheng Ji; Weiqing Qi

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 219 KB
• Volume: 435
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2011.02.048

✦ Synopsis

Let T be a triangular algebra over a commutative ring R. In this paper, under some mild conditions on T , we prove that if

for any x, y ∈ T with xy = 0 (resp. xy = p, where p is the standard idempotent of T ), then δ = d + τ , where d is a derivation of T and τ : T -→ Z(T ) (where Z(T ) is the center of T ) is an R-linear map vanishing at commutators [x, y] with xy = 0 (resp. xy = p).