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Local and $2$-local derivations of simple $n$-ary algebras

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 نشر من قبل Ivan Kaygorodov
 تاريخ النشر 2021
  مجال البحث
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In the present paper, we prove that every local and $2$-local derivation of the complex finite-dimensional simple Filippov algebra is a derivation. As a corollary we have the description of all local and $2$-local derivations of complex finite-dimensional semisimple Filippov algebras. All local derivations of the ternary Malcev algebra $M_8$ are described. It is the first example of a finite-dimensional simple algebra that admits pure local derivations, i.e. algebra admits a local derivation which is not a derivation.



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