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A note on Lie product preserving maps on $Mn(\mathbb{R})$

In: Mathematica Slovaca, vol. 66, no. 3
Janko Marovt
Detaily:
Rok, strany: 2016, 715 - 720
Kľúčové slová:
Lie product, non-linear preserver, commutativity
O článku:
Let $\phi$ be an injective, continuous, Lie product preserving map on $M_n(\mathbb{R)}$, $n>3$. In the paper we show that then there exist an invertible matrix $T\in M_n(\mathbb{R)}$ and a continuous function $\psi: M_n(\mathbb{R})\to \mathbb{R}$, where $\psi(A)=0$ for all matrices of trace zero, such that either $\phi(A)=TAT^{-1}+\psi(A)I$ for all $A\in M_n(\mathbb{R})$, or $\phi(A)=-TA^t T^{-1}+\psi(A)I$ for all $A\in M_n(\mathbb{R})$. We determine that a similar proposition holds true for the set $M_{n}(\mathbb{C})$, $n>3$.
Ako citovať:
ISO 690:
Marovt, J. 2016. A note on Lie product preserving maps on $Mn(\mathbb{R})$. In Mathematica Slovaca, vol. 66, no.3, pp. 715-720. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0173

APA:
Marovt, J. (2016). A note on Lie product preserving maps on $Mn(\mathbb{R})$. Mathematica Slovaca, 66(3), 715-720. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0173
O vydaní:
Publikované: 1. 6. 2016