On additivity of commutator preserving bijections in a matrix algebra
type: Item
instance of: scholarly article
zbMATH Open document ID: 0969.15004
author: A. V. Titov
publication date: 2001-06-10T00:00:00Z
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 1603236
zbMATH Keywords: matrix algebra
zbMATH Keywords: commutator
zbMATH Keywords: bijection
MaRDI profile type: Publication
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title: On additivity of commutator preserving bijections in a matrix algebra
published in: Matematicheskie Zametki YAGU
review text: Let \(M_2^0\) be the set of real \(2\times 2\)-matrices with zero trace. Put \([A,B]=AB-BA\) \((A,B\in M_2^0)\). The main result of the article can be stated as follows: Let \(\varphi\) be a bijection from \(M_2^0\) onto \(M_2^0\) such that \(\varphi([A,B])=[\varphi(A),\varphi(B)]\) for all \(A,B\in M_2^0\). Then \(\varphi(A+B)=\varphi(A)+\varphi(B)\) for all \(A,B\in M_2^0\).
description: scientific article; zbMATH DE number 1603236