Local automorphisms and derivations on 𝕄_{𝕟}

The aim of this note is to give a short proof that 2-local derivations on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M Subscript n"> <mml:semantics> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">M_n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> , the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n times n"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo> × </mml:mo> <mml:mi>n</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">n\times n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> matrix algebra over the complex numbers are derivations and to give a shorter proof that 2-local *-automorphisms on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M Subscript n"> <mml:semantics> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">M_n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are *-automorphisms.

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