(n+1)-Ary derivations os semisimple Filippov algebras

TL;DR

This paper characterizes (n+1)-ary derivations of semisimple Filippov algebras, providing classifications for simple and semisimple cases and introducing new examples of such derivations.

Contribution

It introduces the concept of (n+1)-ary derivations for n-ary algebras and classifies them for semisimple Filippov algebras, including new non-trivial examples.

Findings

Classified (n+1)-ary derivations of simple and semisimple Filippov algebras

Constructed new non-trivial (n+1)-ary derivations

Extended understanding of derivations in n-ary algebra structures

Abstract

We defined (n+1)-ary derivations of $n$-ary algebras. We described (n+1)-derivations of simple and semisimple finite-dimensional Filippov algebras over algebraically closed field zero characteristic. We constructed new examples of non-trivial (n+1)-ary derivations of Filippov algebras.