We introduce Poisson triple systems, which are vector spaces with 3 trilinear operations satisfying 9 polynomial identities of degree 5. We show that every Poisson triple system has a universal enveloping Poisson algebra. Finally, we briefly discuss operadic aspects of Poisson triple systems.

中文翻译：

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泊松三重系统

我们引入了泊松三元组，它是具有 3 个三线性运算的向量空间，满足 9 个 5 次多项式恒等式。我们证明了每个泊松三元组都有一个普遍的包络泊松代数。最后，我们简要讨论泊松三重系统的操作方面。