让$\mathcal{<trans\; data-src="𝒜">𝒜</trans>}$是一个因子von Neumann代数。对于任何$\mathcal{<trans\; data-src="𝒜">𝒜</trans>}<trans\; data-src=",">,</trans>\mathcal{<trans\; data-src="ℬ">ℬ</trans>}<trans\; data-src="\in ">\in </trans>\mathcal{<trans\; data-src="𝒜">𝒜</trans>}$，一种产品${<trans\; data-src="[">[</trans>\mathcal{<trans\; data-src="𝒜">𝒜</trans>}<trans\; data-src=",">,</trans>\mathcal{<trans\; data-src="ℬ">ℬ</trans>}<trans\; data-src="]">]</trans>}_{<trans\; data-src="•">•</trans>}<trans\; data-src="=">=</trans>\mathcal{<trans\; data-src="𝒜">𝒜</trans>}{\mathcal{<trans\; data-src="ℬ">ℬ</trans>}}^{<trans\; data-src="\ast ">\ast </trans>}<trans\; data-src="-">-</trans>\mathcal{<trans\; data-src="ℬ">ℬ</trans>}{\mathcal{<trans\; data-src="𝒜">𝒜</trans>}}^{<trans\; data-src="\ast ">\ast </trans>}$被称为biskew Lie产品。我们证明了每个biskew-Lie三重导子$\mathrm{<trans\; data-src="\psi ">\psi </trans>}<trans\; data-src=":">:</trans>\mathcal{<trans\; data-src="𝒜">𝒜</trans>}<trans\; data-src="\to ">\to </trans>\mathcal{<trans\; data-src="𝒜">𝒜</trans>}$是添加剂$<trans\; data-src="\ast ">\ast </trans>$-推导。