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 languageEnglish
Pages (from-to)1236-1242
Number of pages7
JournalLinear Algebra and Its Applications
Volume430
Issue number4
DOIs
Publication statusPublished - 2009 Feb 1

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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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On generalized Lie derivations of Lie ideals of prime algebras. / Liao, Ping Bao; Liu, Cheng-Kai.

In: Linear Algebra and Its Applications, Vol. 430, No. 4, 01.02.2009, p. 1236-1242.

Research output: Contribution to journalArticle

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AU - Liu, Cheng-Kai

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