Table 1 Nilpotent n -Lie algebras of...

Table 1

Nilpotent n-Lie algebras of class 2	Nonzero multiplications
$A_{n, n + 4,1}$	$[e_{1}, \dots, e_{n}] = e_{n + 3}, [e_{2}, \dots, e_{n + 1}] = e_{n + 4}$
$A_{n, n + 4,2}$	$[e_{1}, \dots, e_{n}] = e_{n + 3}, [e_{3}, \dots, e_{n + 2}] = e_{n + 4} (n \geq 3)$
$A_{n, n + 4,3}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 1}, [e_{2}, \dots, e_{n}, e_{n + 2}] = e_{n + 3}, \\ [e_{1}, e_{3}, \dots, e_{n}, e_{n + 2}] = e_{n + 4} \end{matrix}$
$A_{n, n + 5,1}$	$[e_{1}, \dots, e_{n}] = e_{n + 4}, [e_{2}, \dots, e_{n + 1}] = e_{n + 5}$
$A_{n, n + 5,2}$	$[e_{1}, \dots, e_{n}] = e_{n + 4}, [e_{3}, \dots, e_{n + 2}] = e_{n + 5} (n \geq 3)$
$A_{n, n + 5,3}$	$[e_{1}, \dots, e_{n}] = e_{n + 5}, [e_{4}, \dots, e_{n + 3}] = e_{n + 4} (n \geq 3)$
$A_{n, n + 5,4}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 3}, [e_{2}, \dots, e_{n + 1}] = e_{n + 4}, \\ [e_{1}, e_{3}, \dots, e_{n + 1}] = e_{n + 5} \end{matrix}$
$A_{n, n + 5,5}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 3}, [e_{2}, \dots, e_{n + 1}] = e_{n + 4}, \\ [e_{2}, \dots, e_{n}, e_{n + 2}] = e_{n + 5} \end{matrix}$
$A_{n, n + 5,6}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 3}, [e_{2}, \dots, e_{n + 1}] = e_{n + 4}, \\ [e_{3}, \dots, e_{n + 2}] = e_{n + 5} \end{matrix}$
$A_{n, n + 5,7}$	$\begin{matrix} [e_{1}, \dots, e_{n}] = e_{n + 1}, [e_{1}, e_{2}, e_{4}, \dots, e_{n}, e_{n + 2}] = e_{n + 5}, \\ [e_{1}, e_{3}, \dots, e_{n}, e_{n + 2}] = e_{n + 4}, [e_{2}, \dots, e_{n}, e_{n + 2}] = e_{n + 3} \end{matrix}$

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