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General Preservers of Quasi-Commutativity

Published online by Cambridge University Press:  20 November 2018

Gregor Dolinar  and
Bojan Kuzma
Gregor Dolinar
Affiliation:
Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia e-mail: gregor.dolinar@fe.uni-lj.si
Bojan Kuzma
Affiliation:
University of Primorska, Koper, Slovenia and Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia, e-mail: bojan.kuzma@pef.upr.si
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Abstract

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Let ${{M}_{n}}$ be the algebra of all $n\,\times \,n$ matrices over $\mathbb{C}$. We say that $A,B\in {{M}_{n}}$ quasi-commute if there exists a nonzero $\xi \,\in \,\mathbb{C}$ such that $AB\,=\,\xi BA$. In the paper we classify bijective not necessarily linear maps $\Phi :{{M}_{n}}\to {{M}_{n}}$ which preserve quasi-commutativity in both directions.

Keywords

15A0415A2706A99general preserversmatrix algebraquasi-commutativity
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 4 , 01 August 2010 , pp. 758 - 786
Copyright
Copyright © Canadian Mathematical Society 2010

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