General Preservers of Quasi-Commutativity

Gregor Dolinar, Bojan Kuzma
2010 Canadian Journal of Mathematics - Journal Canadien de Mathematiques  
Let Mn be the algebra of all n × n matrices over C. We say that A, B ∈ Mn quasi-commute if there exists a nonzero ξ ∈ C such that AB = ξBA. In the paper we classify bijective not necessarily linear maps Φ : Mn → Mn which preserve quasi-commutativity in both directions.
doi:10.4153/cjm-2010-041-x fatcat:gfnax46jwrdxtatcaujjgbz3ga