We introduce a Lie triple system associated with the central isotope of (− 1, 1)-algebra. The associator ideal of (−1, 1)-algebra is nilpotent if and only if the Lie triple system is nilpotent. The relationship of the constructed Lie triple system with other known Lie triple systems is discussed.

中文翻译：

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与（−1，1）代数相关的Triple Lie系统

我们介绍与（-1，1）-代数的中心同位素相关的Lie三重系统。（-1，1）-代数的缔合理想是幂等的，当且仅当李三重系统是幂等的。讨论了构造的李三重系统与其他已知李三重系统的关系。