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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 66, Issue 3


A note on Lie product preserving maps on Mn(ℝ)

Janko Marovt
Published Online: 2016-08-26 | DOI: https://doi.org/10.1515/ms-2015-0173


Let ϕ be an injective, continuous, Lie product preserving map on Mn(ℝ), n > 3. In the paper we show that then there exist an invertible matrix TMn(ℝ) and a continuous function ψ:Mn(ℝ)→ ℝ, where ψ(A) = 0 for all matrices of trace zero, such that either ϕ(A) = TAT−1 + ψ(A)I for all AMn(ℝ), or ϕ(A) = −TAtT−1 + ψ(A)I for all AMn(ℝ). We determine that a similar proposition holds true for the set Mn(ℂ), n > 3.

MSC 2010: Primary 47B49; Secondary 15A04, 15A27, 17B60

Keywords: Lie product; non-linear preserver; commutativity


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About the article

Received: 2013-08-13

Accepted: 2013-10-28

Published Online: 2016-08-26

Published in Print: 2016-06-01

Citation Information: Mathematica Slovaca, Volume 66, Issue 3, Pages 715–720, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0173.

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