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 which admits pure local derivations, i.e. algebra admits a local derivation which is not a derivation.

中文翻译：

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简单 n 元代数的局部和 2-局部推导

在本文中，我们证明了复有限维简单 Filippov 代数的每个局部和 2-局部推导都是一个推导。作为推论，我们描述了复数有限维半单 Filippov 代数的所有局部和 2-局部推导。描述了三元 Malcev 代数\(M_8\) 的所有局部推导。它是有限维简单代数的第一个例子，它允许纯局部导数，即代数允许局部导数，它不是一个导数。