\delta-derivations of n-ary algebras

TL;DR

This paper introduces -derivations in n-ary algebras, classifies them for specific algebra types, and provides new examples of non-trivial derivations and antiderivations in these algebraic structures.

Contribution

It defines -derivations for n-ary algebras and describes their structure in key classes, including new explicit examples of non-trivial derivations.

Findings

Classified -derivations of (n+1)-dimensional n-ary Filippov algebras.

Identified -derivations of simple finite-dimensional Filippov algebras and M_8.

Constructed new non-trivial -derivations and antiderivations for Filippov algebras.

Abstract

We defined \delta-derivations of n-ary algebras. We described \delta-derivations of (n+1)-dimensional n-ary Filippov algebras and simple finite-dimensional Filippov algebras over algebraically closed field zero characteristic, and simple ternary Malcev algebra M_8. We constructed new examples of non-trivial \delta-derivations of Filippov algebras and new examples of non-trivial antiderivations of simple Filippov algebras.