Geodesic
General Preservers of Quasi-Commutativity
Canadian journal of mathematics, Tome 62 (2010) no. 4, pp. 758-786

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DOI

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.
DOI : 10.4153/CJM-2010-041-x
Mots-clés : 15A04, 15A27, 06A99, general preservers, matrix algebra, quasi-commutativity 
Dolinar, Gregor; Kuzma, Bojan. General Preservers of Quasi-Commutativity. Canadian journal of mathematics, Tome 62 (2010) no. 4, pp. 758-786. doi: 10.4153/CJM-2010-041-x
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     title = {General {Preservers} of {Quasi-Commutativity}},
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     pages = {758--786},
     year = {2010},
     volume = {62},
     number = {4},
     doi = {10.4153/CJM-2010-041-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-041-x/}
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