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Additive Lie (-Lie) derivations and generalized Lie (-Lie) derivations on nest algebras

✍ Scribed by Xiaofei Qi; Jinchuan Hou

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
186 KB
Volume
431
Category
Article
ISSN
0024-3795

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## Abstract Let __Ξ΄__ be a Lie triple derivation from a nest algebra π’œ into an π’œβ€bimodule ℳ︁. We show that if ℳ︁ is a weak\* closed operator algebra containing π’œ then there are an element __S__ ∈ ℳ︁ and a linear functional __f__ on π’œ such that __Ξ΄__ (__A__) = __SA__ – __AS__ + __f__ (__A__)__I__ fo

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Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f , d : R β†’ A are linear maps satisfying that f ([x, y]) = f (x)yf (y)x + xd(y)yd(x) for all x, y ∈ R, then there exist a generalized de