$n$-ary algebras of the first level

TL;DR

This paper classifies and describes $n$-ary algebras at the first degeneration level, providing detailed classifications specifically for cases where $n=2$ and $n=3$, advancing understanding of their structure.

Contribution

It offers a detailed classification of $n$-ary algebras at the first degeneration level, focusing on the cases $n=2$ and $n=3$, which was previously unexplored.

Findings

Classification of $n$-ary algebras at the first degeneration level

Detailed analysis for $n=2$ and $n=3$ cases

Structural descriptions of these algebras

Abstract

$n$-ary algebras of the first degeneration level are described. A detailed classification is given in the cases $n=2,3$.