Nonlinear lie-type derivations on full matrix algebras

Zhankui Xiao; Feng Wei

doi:10.1007/s00605-012-0388-7

Nonlinear lie-type derivations on full matrix algebras

Zhankui Xiao, Feng Wei^*

^*Corresponding author for this work

School of Mathematics and Statistics

Huaqiao University

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

Let R be a 2-torsion free commutative ring with identity and M_n(R) (n ≥ 2) be the full matrix algebra over R. In this note, we prove that every nonlinear Lie triple derivation on M_n(R) is of the standard form, i. e. it can be expressed as a sum of an inner derivation, an additive induced derivation and a functional annihilating all second commutators of M_n(R). A open conjecture about Lie n-derivations is posed at the end of this note.

Original language	English
Pages (from-to)	77-88
Number of pages	12
Journal	Monatshefte fur Mathematik
Volume	170
Issue number	1
DOIs	https://doi.org/10.1007/s00605-012-0388-7
Publication status	Published - Apr 2013

Keywords

Full matrix algebra
Lie n-derivation
Lie triple derivation

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10.1007/s00605-012-0388-7

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Nonlinear lie-type derivations on full matrix algebras

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Keywords

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