# On generalized Lie derivations of Lie ideals of prime algebras

Ping Bao Liao, Cheng-Kai Liu

Research output: Contribution to journalArticle

12 Citations (Scopus)

### Abstract

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 → A are linear maps satisfying thatf ([x, y]) = f (x) y - f (y) x + xd (y) - yd (x) for all x, y ∈ R,then there exist a generalized derivation g : B → AC + C and a linear map ζ : R → C such that f (x) = g (x) + ζ (x) for all x ∈ R and ζ ([R, R]) = 0 provided that A does not satisfy the standard identity of degree 18.

Original language English 1236-1242 7 Linear Algebra and Its Applications 430 4 https://doi.org/10.1016/j.laa.2008.10.022 Published - 2009 Feb 1

### Fingerprint

Lie Ideal
Linear map
Algebra
Extended Centroid
Generalized Derivation
Subalgebra
Standards

### All Science Journal Classification (ASJC) codes

• Algebra and Number Theory
• Numerical Analysis
• Geometry and Topology
• Discrete Mathematics and Combinatorics

### Cite this

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title = "On generalized Lie derivations of Lie ideals of prime algebras",
abstract = "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 → A are linear maps satisfying thatf ([x, y]) = f (x) y - f (y) x + xd (y) - yd (x) for all x, y ∈ R,then there exist a generalized derivation g : B → AC + C and a linear map ζ : R → C such that f (x) = g (x) + ζ (x) for all x ∈ R and ζ ([R, R]) = 0 provided that A does not satisfy the standard identity of degree 18.",
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In: Linear Algebra and Its Applications, Vol. 430, No. 4, 01.02.2009, p. 1236-1242.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On generalized Lie derivations of Lie ideals of prime algebras

AU - Liao, Ping Bao

AU - Liu, Cheng-Kai

PY - 2009/2/1

Y1 - 2009/2/1

N2 - 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 → A are linear maps satisfying thatf ([x, y]) = f (x) y - f (y) x + xd (y) - yd (x) for all x, y ∈ R,then there exist a generalized derivation g : B → AC + C and a linear map ζ : R → C such that f (x) = g (x) + ζ (x) for all x ∈ R and ζ ([R, R]) = 0 provided that A does not satisfy the standard identity of degree 18.

AB - 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 → A are linear maps satisfying thatf ([x, y]) = f (x) y - f (y) x + xd (y) - yd (x) for all x, y ∈ R,then there exist a generalized derivation g : B → AC + C and a linear map ζ : R → C such that f (x) = g (x) + ζ (x) for all x ∈ R and ζ ([R, R]) = 0 provided that A does not satisfy the standard identity of degree 18.

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