Table 2 Nilpotent n -Lie algebras of...

Table 2

Nilpotent n-Lie algebras of class 2	Nonzero multiplications
$A_{n, n + 6,1}$	$[e_{1}, \dots, e_{n}] = e_{n + 5}, [e_{5}, \dots, e_{n + 4}] = e_{n + 6}$
$A_{n, n + 6,2}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 4}, [e_{2}, \dots, e_{n + 1}] = e_{n + 5}, \\ [e_{3}, \dots, e_{n}, e_{n + 2}, e_{n + 3}] = e_{n + 6} \end{matrix}$
$A_{n, n + 6,3}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 4}, [e_{2}, \dots, e_{n + 1}] = e_{n + 5}, \\ [e_{1}, e_{4}, \dots, e_{n}, e_{n + 2}, e_{n + 3}] = e_{n + 6} \end{matrix}$
$A_{n, n + 6,4}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 4}, [e_{2}, \dots, e_{n + 1}] = e_{n + 5}, \\ [e_{1}, e_{5}, \dots, e_{n + 3}] = e_{n + 6} \end{matrix}$
$A_{n, n + 6,5}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 4}, [e_{3}, \dots, e_{n + 2}] = e_{n + 5}, \\ [e_{2}, e_{4}, \dots, e_{n + 1}, e_{n + 3}] = e_{n + 6} \end{matrix}$
$A_{n, n + 6,6}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 4}, [e_{3}, \dots, e_{n + 2}] = e_{n + 5}, \\ [e_{1}, e_{2}, e_{5}, \dots, e_{n + 1}, e_{n + 3}] = e_{n + 6} \end{matrix}$
$A_{n, n + 6,7}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 3}, [e_{2}, \dots, e_{n + 1}] = e_{n + 4}, \\ [e_{1}, e_{3}, \dots, e_{n + 1}] = e_{n + 5}, [e_{3}, \dots, e_{n + 2}] = e_{n + 6} \end{matrix}$
$A_{n, n + 6,8}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 3}, [e_{2}, \dots, e_{n + 1}] = e_{n + 4}, \\ [e_{1}, e_{3}, \dots, e_{n + 1}] = e_{n + 5}, [e_{2}, e_{4}, \dots, e_{n + 2}] = e_{n + 6} \end{matrix}$
$A_{n, n + 6,9}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 3}, [e_{2}, \dots, e_{n + 1}] = e_{n + 4}, \\ [e_{1}, e_{3}, \dots, e_{n + 1}] = e_{n + 5}, [e_{1}, e_{2}, e_{5}, \dots, e_{n + 2}] = e_{n + 6} \end{matrix}$
$A_{n, n + 6,10}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 3}, [e_{2}, \dots, e_{n + 1}] = e_{n + 4}, \\ [e_{2}, \dots, e_{n}, e_{n + 2}] = e_{n + 5}, [e_{1}, e_{4}, \dots, e_{n + 2}] = e_{n + 6} \end{matrix}$
$A_{n, n + 6,11}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 3}, [e_{2}, \dots, e_{n + 1}] = e_{n + 4}, \\ [e_{3}, \dots, e_{n + 2}] = e_{n + 5}, [e_{1}, e_{3}, \dots, e_{n}, e_{n + 2}] = e_{n + 6} \end{matrix}$
$A_{n, n + 6,12}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 3}, [e_{2}, \dots, e_{n + 1}] = e_{n + 4}, \\ [e_{3}, \dots, e_{n + 2}] = e_{n + 5}, [e_{1}, e_{2}, e_{4}, \dots, e_{n}, e_{n + 2}] = e_{n + 6} \end{matrix}$
$A_{n, n + 6,13}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 3}, [e_{2}, \dots, e_{n + 1}] = e_{n + 4}, \\ [e_{3}, \dots, e_{n + 2}] = e_{n + 5}, [e_{1}, e_{2}, e_{5}, \dots, e_{n + 2}] = e_{n + 6} \end{matrix}$
$A_{n, n + 6,14}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 1}, [e_{2}, \dots, e_{n}, e_{n + 2}] = e_{n + 3}, \\ [e_{1}, e_{3}, \dots, e_{n}, e_{n + 2}] = e_{n + 4}, [e_{3}, \dots, e_{n + 2}] = e_{n + 5}, \\ [e_{1}, e_{3}, \dots, e_{n}, e_{n + 2}] = e_{n + 6} \end{matrix}$

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