On additivity of commutator preserving bijections in a matrix algebra
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 \(A,B\in M_2^0\).
scientific article; zbMATH DE number 1603236